0.07/0.12 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.07/0.15 % Command : run_portfolio.sh /export/starexec/sandbox/benchmark/theBenchmark.p /export/starexec/sandbox/tmp/tmp.pX90fzGHXm 0.15/0.36 % Computer : n014.cluster.edu 0.15/0.36 % Model : x86_64 x86_64 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.15/0.36 % Memory : 8042.1875MB 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64 0.15/0.36 % CPULimit : 960 0.15/0.36 % DateTime : Thu Jul 2 08:42:55 EDT 2020 0.15/0.36 % CPUTime : 0.15/0.36 % Running portfolio for 120 s 0.15/0.36 % File : /export/starexec/sandbox/benchmark/theBenchmark.p 0.15/0.36 % Number of cores: 8 0.15/0.37 % Python version: Python 3.6.8 0.15/0.37 % Running in HO mode 0.56/0.66 % Estimated wc time : 1286 0.56/0.66 % Estimated cpu time (7 cpus) : 183.71428571428572 0.58/0.72 % /export/starexec/sandbox/solver/bin/lams/s6.sh running for 21s 0.58/0.74 % /export/starexec/sandbox/solver/bin/lams/new_b3.2.norw.sh running for 15s 0.58/0.75 % /export/starexec/sandbox/solver/bin/lams/b.rpo.sh running for 21s 0.58/0.75 % /export/starexec/sandbox/solver/bin/lams/c.s.2.sh running for 68s 0.58/0.75 % /export/starexec/sandbox/solver/bin/lams/s6.ds.sh running for 10s 0.58/0.75 % /export/starexec/sandbox/solver/bin/lams/c.easy.sh running for 26s 0.58/0.75 % /export/starexec/sandbox/solver/bin/lams/old_b3.avatar.sh running for 15s 69.86/10.64 % /export/starexec/sandbox/solver/bin/lams/old_sp2.sh running for 17s 105.63/15.83 % /export/starexec/sandbox/solver/bin/lams/b.sh running for 31s 105.63/15.84 % /export/starexec/sandbox/solver/bin/lams/sh1.sh running for 26s 145.91/21.65 % /export/starexec/sandbox/solver/bin/lams/b.lsimp.sh running for 17s 146.76/21.77 % /export/starexec/sandbox/solver/bin/lams/b.split.sh running for 31s 182.21/26.97 % /export/starexec/sandbox/solver/bin/lams/s4.sh running for 15s 187.18/27.76 % /export/starexec/sandbox/solver/bin/lams/b.rw.sh running for 26s 188.83/28.03 % /export/starexec/sandbox/solver/bin/lams/c_ic.sh running for 42s 189.04/28.10 % /export/starexec/sandbox/solver/bin/lams/s1.f.sh running for 15s 236.33/34.79 % Solved by lams/b.rw.sh. 236.33/34.79 % Running : timeout 17 /export/starexec/sandbox/solver/bin/lams/eprover-ho --pos-ext=all --neg-ext=all /export/starexec/sandbox/tmp/tmp.pX90fzGHXm/e_input648dee --cpu-limit=15 --auto -s -p. 236.33/34.79 % done 485 iterations in 6.585s 236.33/34.79 % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p' 236.33/34.79 % SZS output start Refutation 236.33/34.79 tff(ex1E1, axiom, ex1E1 <=> 236.33/34.79 (![A,Xphi:(($i > $o))]: 236.33/34.79 (ex1(A,^[Xx]: Xphi(Xx)) => (?[Xx]: (Xphi(Xx) & in(Xx,A)))))). 236.33/34.79 tff('0', plain, 236.33/34.79 ex1E1 = 236.33/34.79 (![X4,X6:(($i > $o))]: 236.33/34.79 (ex1(X4,^[V_1]: X6(V_1)) => (?[X8]: (X6(X8) & in(X8,X4))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(ex1, axiom, ex1() = 236.33/34.79 ^[A,Xphi:(($i > $o))]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))). 236.33/34.79 tff(singleton, axiom, singleton() = 236.33/34.79 ^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))). 236.33/34.79 tff('1', plain, 236.33/34.79 singleton = (^[A]: (?[Xx]: ((A = setadjoin(Xx,emptyset)) & in(Xx,A)))), 236.33/34.79 inference('simplify_rw_rule', [status(thm)], [singleton])). 236.33/34.79 tff('2', plain, 236.33/34.79 singleton = 236.33/34.79 (^[V_1]: (?[X4]: ((V_1 = setadjoin(X4,emptyset)) & in(X4,V_1)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff('3', plain, 236.33/34.79 ex1 = (^[A,Xphi:(($i > $o))]: singleton(dsetconstr(A,^[Xx]: Xphi(Xx)))), 236.33/34.79 inference('simplify_rw_rule', [status(thm)], [ex1, '2'])). 236.33/34.79 tff('4', plain, 236.33/34.79 ex1 = 236.33/34.79 (^[V_1,V_2:(($i > $o))]: singleton(dsetconstr(V_1,^[V_3]: V_2(V_3)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(singletonprop, axiom, singletonprop <=> 236.33/34.79 (![A,Xphi:(($i > $o))]: 236.33/34.79 ((![Xx]: 236.33/34.79 (in(Xx,A) => 236.33/34.79 (![Xy]: (in(Xy,A) => (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))) => 236.33/34.79 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 236.33/34.79 singleton(dsetconstr(A,^[Xx]: Xphi(Xx))))))). 236.33/34.79 tff('5', plain, 236.33/34.79 singletonprop = 236.33/34.79 (![X4,X6:(($i > $o))]: 236.33/34.79 ((![X8]: 236.33/34.79 (in(X8,X4) => 236.33/34.79 (![X10]: (in(X10,X4) => (X6(X8) => (X6(X10) => (X8 = X10))))))) => 236.33/34.79 ((?[X12]: (X6(X12) & in(X12,X4))) => 236.33/34.79 singleton(dsetconstr(X4,^[V_1]: X6(V_1)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setunionsingleton, axiom, setunionsingleton <=> 236.33/34.79 (![Xx]: (setunion(setadjoin(Xx,emptyset)) = Xx))). 236.33/34.79 tff('6', plain, 236.33/34.79 setunionsingleton = (![X4]: (setunion(setadjoin(X4,emptyset)) = X4)), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setunionsingleton2, axiom, setunionsingleton2 <=> 236.33/34.79 (![A]: subset(A,setunion(setadjoin(A,emptyset))))). 236.33/34.79 tff('7', plain, 236.33/34.79 setunionsingleton2 = (![X4]: subset(X4,setunion(setadjoin(X4,emptyset)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setunionsingleton1, axiom, setunionsingleton1 <=> 236.33/34.79 (![A]: subset(setunion(setadjoin(A,emptyset)),A))). 236.33/34.79 tff('8', plain, 236.33/34.79 setunionsingleton1 = (![X4]: subset(setunion(setadjoin(X4,emptyset)),X4)), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setunionE2, axiom, setunionE2 <=> 236.33/34.79 (![A,Xx]: (in(Xx,setunion(A)) => (?[X]: (in(Xx,X) & in(X,A)))))). 236.33/34.79 tff('9', plain, 236.33/34.79 setunionE2 = 236.33/34.79 (![X4,X6]: (in(X6,setunion(X4)) => (?[X8]: (in(X6,X8) & in(X8,X4))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(cartprodmempair, axiom, cartprodmempair <=> 236.33/34.79 (![A,B,Xu]: (in(Xu,cartprod(A,B)) => iskpair(Xu)))). 236.33/34.79 tff('10', plain, 236.33/34.79 cartprodmempair = (![X4,X6,X8]: (in(X8,cartprod(X4,X6)) => iskpair(X8))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(cartprodmempair1, axiom, cartprodmempair1 <=> 236.33/34.79 (![A,B,Xu]: 236.33/34.79 (in(Xu,cartprod(A,B)) => 236.33/34.79 (?[Xx]: ((?[Xy]: ((Xu = kpair(Xx,Xy)) & in(Xy,B))) & in(Xx,A)))))). 236.33/34.79 tff('11', plain, 236.33/34.79 cartprodmempair1 = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,cartprod(X4,X6)) => 236.33/34.79 (?[X10]: 236.33/34.79 ((?[X12]: ((X8 = kpair(X10,X12)) & in(X12,X6))) & in(X10,X4))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(cartprodpairin, axiom, cartprodpairin <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,A) => (![Xy]: (in(Xy,B) => in(kpair(Xx,Xy),cartprod(A,B))))))). 236.33/34.79 tff('12', plain, 236.33/34.79 cartprodpairin = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,X4) => 236.33/34.79 (![X10]: (in(X10,X6) => in(kpair(X8,X10),cartprod(X4,X6)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(ubforcartprodlem3, axiom, ubforcartprodlem3 <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,A) => 236.33/34.79 (![Xy]: 236.33/34.79 (in(Xy,B) => in(kpair(Xx,Xy),powerset(powerset(binunion(A,B))))))))). 236.33/34.79 tff('13', plain, 236.33/34.79 ubforcartprodlem3 = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,X4) => 236.33/34.79 (![X10]: 236.33/34.79 (in(X10,X6) => 236.33/34.79 in(kpair(X8,X10),powerset(powerset(binunion(X4,X6)))))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(ubforcartprodlem2, axiom, ubforcartprodlem2 <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,A) => 236.33/34.79 (![Xy]: 236.33/34.79 (in(Xy,B) => 236.33/34.79 in(setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 236.33/34.79 emptyset)), 236.33/34.79 powerset(powerset(binunion(A,B))))))))). 236.33/34.79 tff('14', plain, 236.33/34.79 ubforcartprodlem2 = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,X4) => 236.33/34.79 (![X10]: 236.33/34.79 (in(X10,X6) => 236.33/34.79 in(setadjoin(setadjoin(X8,emptyset), 236.33/34.79 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 236.33/34.79 emptyset)), 236.33/34.79 powerset(powerset(binunion(X4,X6)))))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(ubforcartprodlem1, axiom, ubforcartprodlem1 <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,A) => 236.33/34.79 (![Xy]: 236.33/34.79 (in(Xy,B) => 236.33/34.79 subset(setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 236.33/34.79 emptyset)), 236.33/34.79 powerset(binunion(A,B)))))))). 236.33/34.79 tff('15', plain, 236.33/34.79 ubforcartprodlem1 = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,X4) => 236.33/34.79 (![X10]: 236.33/34.79 (in(X10,X6) => 236.33/34.79 subset(setadjoin(setadjoin(X8,emptyset), 236.33/34.79 setadjoin(setadjoin(X8,setadjoin(X10,emptyset)), 236.33/34.79 emptyset)), 236.33/34.79 powerset(binunion(X4,X6))))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(upairinpowunion, axiom, upairinpowunion <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,A) => 236.33/34.79 (![Xy]: 236.33/34.79 (in(Xy,B) => 236.33/34.79 in(setadjoin(Xx,setadjoin(Xy,emptyset)),powerset(binunion(A,B)))))))). 236.33/34.79 tff('16', plain, 236.33/34.79 upairinpowunion = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,X4) => 236.33/34.79 (![X10]: 236.33/34.79 (in(X10,X6) => 236.33/34.79 in(setadjoin(X8,setadjoin(X10,emptyset)), 236.33/34.79 powerset(binunion(X4,X6))))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(upairsubunion, axiom, upairsubunion <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,A) => 236.33/34.79 (![Xy]: 236.33/34.79 (in(Xy,B) => 236.33/34.79 subset(setadjoin(Xx,setadjoin(Xy,emptyset)),binunion(A,B))))))). 236.33/34.79 tff('17', plain, 236.33/34.79 upairsubunion = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,X4) => 236.33/34.79 (![X10]: 236.33/34.79 (in(X10,X6) => 236.33/34.79 subset(setadjoin(X8,setadjoin(X10,emptyset)),binunion(X4,X6)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(upairset2E, axiom, upairset2E <=> 236.33/34.79 (![Xx,Xy,Xz]: 236.33/34.79 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 236.33/34.79 tff('18', plain, 236.33/34.79 upairset2E = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 236.33/34.79 ((X8 = X4) | (X8 = X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(singletoninpowunion, axiom, singletoninpowunion <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(binunion(A,B)))))). 236.33/34.79 tff('19', plain, 236.33/34.79 singletoninpowunion = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,X4) => in(setadjoin(X8,emptyset),powerset(binunion(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(singletoninpowerset, axiom, singletoninpowerset <=> 236.33/34.79 (![A,Xx]: (in(Xx,A) => in(setadjoin(Xx,emptyset),powerset(A))))). 236.33/34.79 tff('20', plain, 236.33/34.79 singletoninpowerset = 236.33/34.79 (![X4,X6]: (in(X6,X4) => in(setadjoin(X6,emptyset),powerset(X4)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(singletonsubset, axiom, singletonsubset <=> 236.33/34.79 (![A,Xx]: (in(Xx,A) => subset(setadjoin(Xx,emptyset),A)))). 236.33/34.79 tff('21', plain, 236.33/34.79 singletonsubset = 236.33/34.79 (![X4,X6]: (in(X6,X4) => subset(setadjoin(X6,emptyset),X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(kpairp, axiom, kpairp <=> (![Xx,Xy]: iskpair(kpair(Xx,Xy)))). 236.33/34.79 tff('22', plain, kpairp = (![X4,X6]: iskpair(kpair(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(kpair, axiom, kpair() = 236.33/34.79 ^[Xx,Xy]: 236.33/34.79 setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))). 236.33/34.79 tff('23', plain, 236.33/34.79 kpair = 236.33/34.79 (^[Xx,Xy]: 236.33/34.79 setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)),emptyset))), 236.33/34.79 inference('simplify_rw_rule', [status(thm)], [kpair])). 236.33/34.79 tff('24', plain, 236.33/34.79 kpair = 236.33/34.79 (^[V_1,V_2]: 236.33/34.79 setadjoin(setadjoin(V_1,emptyset), 236.33/34.79 setadjoin(setadjoin(V_1,setadjoin(V_2,emptyset)),emptyset))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(kpairiskpair, axiom, kpairiskpair <=> 236.33/34.79 (![Xx,Xy]: 236.33/34.79 iskpair(setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 236.33/34.79 emptyset))))). 236.33/34.79 tff('25', plain, 236.33/34.79 kpairiskpair = 236.33/34.79 (![X4,X6]: 236.33/34.79 iskpair(setadjoin(setadjoin(X4,emptyset), 236.33/34.79 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 236.33/34.79 emptyset)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setukpairIR, axiom, setukpairIR <=> 236.33/34.79 (![Xx,Xy]: 236.33/34.79 in(Xy, 236.33/34.79 setunion(setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 236.33/34.79 emptyset)))))). 236.33/34.79 tff('26', plain, 236.33/34.79 setukpairIR = 236.33/34.79 (![X4,X6]: 236.33/34.79 in(X6, 236.33/34.79 setunion(setadjoin(setadjoin(X4,emptyset), 236.33/34.79 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 236.33/34.79 emptyset))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setukpairIL, axiom, setukpairIL <=> 236.33/34.79 (![Xx,Xy]: 236.33/34.79 in(Xx, 236.33/34.79 setunion(setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 236.33/34.79 emptyset)))))). 236.33/34.79 tff('27', plain, 236.33/34.79 setukpairIL = 236.33/34.79 (![X4,X6]: 236.33/34.79 in(X4, 236.33/34.79 setunion(setadjoin(setadjoin(X4,emptyset), 236.33/34.79 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 236.33/34.79 emptyset))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(secondinupair, axiom, secondinupair <=> 236.33/34.79 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 236.33/34.79 tff('28', plain, 236.33/34.79 secondinupair = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(iskpair, axiom, iskpair() = 236.33/34.79 ^[A]: 236.33/34.79 (?[Xx]: 236.33/34.79 ((?[Xy]: 236.33/34.79 ((A = 236.33/34.79 setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 236.33/34.79 emptyset))) & 236.33/34.79 in(Xy,setunion(A)))) & 236.33/34.79 in(Xx,setunion(A))))). 236.33/34.79 tff('29', plain, 236.33/34.79 iskpair = 236.33/34.79 (^[A]: 236.33/34.79 (?[Xx]: 236.33/34.79 ((?[Xy]: 236.33/34.79 ((A = 236.33/34.79 setadjoin(setadjoin(Xx,emptyset), 236.33/34.79 setadjoin(setadjoin(Xx,setadjoin(Xy,emptyset)), 236.33/34.79 emptyset))) & 236.33/34.79 in(Xy,setunion(A)))) & 236.33/34.79 in(Xx,setunion(A))))), 236.33/34.79 inference('simplify_rw_rule', [status(thm)], [iskpair])). 236.33/34.79 tff('30', plain, 236.33/34.79 iskpair = 236.33/34.79 (^[V_1]: 236.33/34.79 (?[X4]: 236.33/34.79 ((?[X6]: 236.33/34.79 ((V_1 = 236.33/34.79 setadjoin(setadjoin(X4,emptyset), 236.33/34.79 setadjoin(setadjoin(X4,setadjoin(X6,emptyset)), 236.33/34.79 emptyset))) & 236.33/34.79 in(X6,setunion(V_1)))) & 236.33/34.79 in(X4,setunion(V_1))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(symdiffIneg2, axiom, symdiffIneg2 <=> 236.33/34.79 (![A,B,Xx]: ((~in(Xx,A)) => ((~in(Xx,B)) => (~in(Xx,symdiff(A,B))))))). 236.33/34.79 tff('31', plain, 236.33/34.79 symdiffIneg2 = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 ((~in(X8,X4)) => ((~in(X8,X6)) => (~in(X8,symdiff(X4,X6)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(symdiffIneg1, axiom, symdiffIneg1 <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => (~in(Xx,symdiff(A,B))))))). 236.33/34.79 tff('32', plain, 236.33/34.79 symdiffIneg1 = 236.33/34.79 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => (~in(X8,symdiff(X4,X6)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(symdiffI2, axiom, symdiffI2 <=> 236.33/34.79 (![A,B,Xx]: ((~in(Xx,A)) => (in(Xx,B) => in(Xx,symdiff(A,B)))))). 236.33/34.79 tff('33', plain, 236.33/34.79 symdiffI2 = 236.33/34.79 (![X4,X6,X8]: ((~in(X8,X4)) => (in(X8,X6) => in(X8,symdiff(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(symdiffI1, axiom, symdiffI1 <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,symdiff(A,B)))))). 236.33/34.79 tff('34', plain, 236.33/34.79 symdiffI1 = 236.33/34.79 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,symdiff(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(symdiffE, axiom, symdiffE <=> 236.33/34.79 (![A,B,Xx]: 236.33/34.79 (in(Xx,symdiff(A,B)) => 236.33/34.79 (![Xphi:$o]: 236.33/34.79 ((in(Xx,A) => ((~in(Xx,B)) => Xphi)) => 236.33/34.79 (((~in(Xx,A)) => (in(Xx,B) => Xphi)) => Xphi)))))). 236.33/34.79 tff('35', plain, 236.33/34.79 symdiffE = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (in(X8,symdiff(X4,X6)) => 236.33/34.79 (![X10:$o]: 236.33/34.79 ((in(X8,X4) => ((~in(X8,X6)) => X10)) => 236.33/34.79 (((~in(X8,X4)) => (in(X8,X6) => X10)) => X10))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusSubset1, axiom, setminusSubset1 <=> 236.33/34.79 (![A,B]: ((setminus(A,B) = emptyset) => subset(A,B)))). 236.33/34.79 tff('36', plain, 236.33/34.79 setminusSubset1 = 236.33/34.79 (![X4,X6]: ((setminus(X4,X6) = emptyset) => subset(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusLsub, axiom, setminusLsub <=> (![A,B]: subset(setminus(A,B),A))). 236.33/34.79 tff('37', plain, setminusLsub = (![X4,X6]: subset(setminus(X4,X6),X4)), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusIRneg, axiom, setminusIRneg <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,B) => (~in(Xx,setminus(A,B)))))). 236.33/34.79 tff('38', plain, 236.33/34.79 setminusIRneg = (![X4,X6,X8]: (in(X8,X6) => (~in(X8,setminus(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusILneg, axiom, setminusILneg <=> 236.33/34.79 (![A,B,Xx]: ((~in(Xx,A)) => (~in(Xx,setminus(A,B)))))). 236.33/34.79 tff('39', plain, 236.33/34.79 setminusILneg = 236.33/34.79 (![X4,X6,X8]: ((~in(X8,X4)) => (~in(X8,setminus(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusELneg, axiom, setminusELneg <=> 236.33/34.79 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => ((~in(Xx,B)) => (~in(Xx,A)))))). 236.33/34.79 tff('40', plain, 236.33/34.79 setminusELneg = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 ((~in(X8,setminus(X4,X6))) => ((~in(X8,X6)) => (~in(X8,X4))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusERneg, axiom, setminusERneg <=> 236.33/34.79 (![A,B,Xx]: ((~in(Xx,setminus(A,B))) => (in(Xx,A) => in(Xx,B))))). 236.33/34.79 tff('41', plain, 236.33/34.79 setminusERneg = 236.33/34.79 (![X4,X6,X8]: ((~in(X8,setminus(X4,X6))) => (in(X8,X4) => in(X8,X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusSubset2, axiom, setminusSubset2 <=> 236.33/34.79 (![A,B]: (subset(A,B) => (setminus(A,B) = emptyset)))). 236.33/34.79 tff('42', plain, 236.33/34.79 setminusSubset2 = 236.33/34.79 (![X4,X6]: (subset(X4,X6) => (setminus(X4,X6) = emptyset))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusER, axiom, setminusER <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,setminus(A,B)) => (~in(Xx,B))))). 236.33/34.79 tff('43', plain, 236.33/34.79 setminusER = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => (~in(X8,X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusEL, axiom, setminusEL <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,setminus(A,B)) => in(Xx,A)))). 236.33/34.79 tff('44', plain, 236.33/34.79 setminusEL = (![X4,X6,X8]: (in(X8,setminus(X4,X6)) => in(X8,X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setminusI, axiom, setminusI <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => in(Xx,setminus(A,B)))))). 236.33/34.79 tff('45', plain, 236.33/34.79 setminusI = 236.33/34.79 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => in(X8,setminus(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(bs114d, axiom, bs114d <=> 236.33/34.79 (![A,B,C]: 236.33/34.79 (binintersect(A,binunion(B,C)) = 236.33/34.79 binunion(binintersect(A,B),binintersect(A,C))))). 236.33/34.79 tff('46', plain, 236.33/34.79 bs114d = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (binintersect(X4,binunion(X6,X8)) = 236.33/34.79 binunion(binintersect(X4,X6),binintersect(X4,X8)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectSubset1, axiom, binintersectSubset1 <=> 236.33/34.79 (![A,B]: ((binintersect(A,B) = A) => subset(A,B)))). 236.33/34.79 tff('47', plain, 236.33/34.79 binintersectSubset1 = 236.33/34.79 (![X4,X6]: ((binintersect(X4,X6) = X4) => subset(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectSubset4, axiom, binintersectSubset4 <=> 236.33/34.79 (![A,B]: (subset(B,A) => (binintersect(A,B) = B)))). 236.33/34.79 tff('48', plain, 236.33/34.79 binintersectSubset4 = 236.33/34.79 (![X4,X6]: (subset(X6,X4) => (binintersect(X4,X6) = X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectRsub, axiom, binintersectRsub <=> 236.33/34.79 (![A,B]: subset(binintersect(A,B),B))). 236.33/34.79 tff('49', plain, 236.33/34.79 binintersectRsub = (![X4,X6]: subset(binintersect(X4,X6),X6)), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(disjointsetsI1, axiom, disjointsetsI1 <=> 236.33/34.79 (![A,B]: 236.33/34.79 ((~(?[Xx]: (in(Xx,B) & in(Xx,A)))) => (binintersect(A,B) = emptyset)))). 236.33/34.79 tff('50', plain, 236.33/34.79 disjointsetsI1 = 236.33/34.79 (![X4,X6]: 236.33/34.79 ((~(?[X8]: (in(X8,X6) & in(X8,X4)))) => 236.33/34.79 (binintersect(X4,X6) = emptyset))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectER, axiom, binintersectER <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,B)))). 236.33/34.79 tff('51', plain, 236.33/34.79 binintersectER = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectSubset3, axiom, binintersectSubset3 <=> 236.33/34.79 (![A,B]: ((binintersect(A,B) = B) => subset(B,A)))). 236.33/34.79 tff('52', plain, 236.33/34.79 binintersectSubset3 = 236.33/34.79 (![X4,X6]: ((binintersect(X4,X6) = X6) => subset(X6,X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectSubset2, axiom, binintersectSubset2 <=> 236.33/34.79 (![A,B]: (subset(A,B) => (binintersect(A,B) = A)))). 236.33/34.79 tff('53', plain, 236.33/34.79 binintersectSubset2 = 236.33/34.79 (![X4,X6]: (subset(X4,X6) => (binintersect(X4,X6) = X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectLsub, axiom, binintersectLsub <=> 236.33/34.79 (![A,B]: subset(binintersect(A,B),A))). 236.33/34.79 tff('54', plain, 236.33/34.79 binintersectLsub = (![X4,X6]: subset(binintersect(X4,X6),X4)), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectEL, axiom, binintersectEL <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,binintersect(A,B)) => in(Xx,A)))). 236.33/34.79 tff('55', plain, 236.33/34.79 binintersectEL = (![X4,X6,X8]: (in(X8,binintersect(X4,X6)) => in(X8,X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectSubset5, axiom, binintersectSubset5 <=> 236.33/34.79 (![A,B,C]: (subset(C,A) => (subset(C,B) => subset(C,binintersect(A,B)))))). 236.33/34.79 tff('56', plain, 236.33/34.79 binintersectSubset5 = 236.33/34.79 (![X4,X6,X8]: 236.33/34.79 (subset(X8,X4) => (subset(X8,X6) => subset(X8,binintersect(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binintersectI, axiom, binintersectI <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,A) => (in(Xx,B) => in(Xx,binintersect(A,B)))))). 236.33/34.79 tff('57', plain, 236.33/34.79 binintersectI = 236.33/34.79 (![X4,X6,X8]: (in(X8,X4) => (in(X8,X6) => in(X8,binintersect(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binunionRsub, axiom, binunionRsub <=> (![A,B]: subset(B,binunion(A,B)))). 236.33/34.79 tff('58', plain, binunionRsub = (![X4,X6]: subset(X6,binunion(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binunionLsub, axiom, binunionLsub <=> (![A,B]: subset(A,binunion(A,B)))). 236.33/34.79 tff('59', plain, binunionLsub = (![X4,X6]: subset(X4,binunion(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binunionE, axiom, binunionE <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,binunion(A,B)) => (in(Xx,A) | in(Xx,B))))). 236.33/34.79 tff('60', plain, 236.33/34.79 binunionE = 236.33/34.79 (![X4,X6,X8]: (in(X8,binunion(X4,X6)) => (in(X8,X4) | in(X8,X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binunionEcases, axiom, binunionEcases <=> 236.33/34.79 (![A,B,Xx,Xphi:$o]: 236.33/34.79 (in(Xx,binunion(A,B)) => 236.33/34.79 ((in(Xx,A) => Xphi) => ((in(Xx,B) => Xphi) => Xphi))))). 236.33/34.79 tff('61', plain, 236.33/34.79 binunionEcases = 236.33/34.79 (![X4,X6,X8,X10:$o]: 236.33/34.79 (in(X8,binunion(X4,X6)) => 236.33/34.79 ((in(X8,X4) => X10) => ((in(X8,X6) => X10) => X10)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binunionIR, axiom, binunionIR <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,B) => in(Xx,binunion(A,B))))). 236.33/34.79 tff('62', plain, 236.33/34.79 binunionIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,binunion(X4,X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(upairset2IR, axiom, upairset2IR <=> 236.33/34.79 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 236.33/34.79 tff('63', plain, 236.33/34.79 upairset2IR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(binunionIL, axiom, binunionIL <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,A) => in(Xx,binunion(A,B))))). 236.33/34.79 tff('64', plain, 236.33/34.79 binunionIL = (![X4,X6,X8]: (in(X8,X4) => in(X8,binunion(X4,X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(sepSubset, axiom, sepSubset <=> 236.33/34.79 (![A,Xphi:(($i > $o))]: subset(dsetconstr(A,^[Xx]: Xphi(Xx)),A))). 236.33/34.79 tff('65', plain, 236.33/34.79 sepSubset = 236.33/34.79 (![X4,X6:(($i > $o))]: subset(dsetconstr(X4,^[V_1]: X6(V_1)),X4)), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(sepInPowerset, axiom, sepInPowerset <=> 236.33/34.79 (![A,Xphi:(($i > $o))]: in(dsetconstr(A,^[Xx]: Xphi(Xx)),powerset(A)))). 236.33/34.79 tff('66', plain, 236.33/34.79 sepInPowerset = 236.33/34.79 (![X4,X6:(($i > $o))]: in(dsetconstr(X4,^[V_1]: X6(V_1)),powerset(X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(powersetsubset, axiom, powersetsubset <=> 236.33/34.79 (![A,B]: (subset(A,B) => subset(powerset(A),powerset(B))))). 236.33/34.79 tff('67', plain, 236.33/34.79 powersetsubset = 236.33/34.79 (![X4,X6]: (subset(X4,X6) => subset(powerset(X4),powerset(X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(inPowerset, axiom, inPowerset <=> (![A]: in(A,powerset(A)))). 236.33/34.79 tff('68', plain, inPowerset = (![X4]: in(X4,powerset(X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(powersetE1, axiom, powersetE1 <=> 236.33/34.79 (![A,B]: (in(B,powerset(A)) => subset(B,A)))). 236.33/34.79 tff('69', plain, 236.33/34.79 powersetE1 = (![X4,X6]: (in(X6,powerset(X4)) => subset(X6,X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(powersetI1, axiom, powersetI1 <=> 236.33/34.79 (![A,B]: (subset(B,A) => in(B,powerset(A))))). 236.33/34.79 tff('70', plain, 236.33/34.79 powersetI1 = (![X4,X6]: (subset(X6,X4) => in(X6,powerset(X4)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subsetemptysetimpeq, axiom, subsetemptysetimpeq <=> 236.33/34.79 (![A]: (subset(A,emptyset) => (A = emptyset)))). 236.33/34.79 tff('71', plain, 236.33/34.79 subsetemptysetimpeq = (![X4]: (subset(X4,emptyset) => (X4 = emptyset))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setextsub, axiom, setextsub <=> 236.33/34.79 (![A,B]: (subset(A,B) => (subset(B,A) => (A = B))))). 236.33/34.79 tff('72', plain, 236.33/34.79 setextsub = (![X4,X6]: (subset(X4,X6) => (subset(X6,X4) => (X4 = X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subset2powerset, axiom, subset2powerset <=> 236.33/34.79 (![A,B]: (subset(A,B) => in(A,powerset(B))))). 236.33/34.79 tff('73', plain, 236.33/34.79 subset2powerset = (![X4,X6]: (subset(X4,X6) => in(X4,powerset(X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setadjoinSub2, axiom, setadjoinSub2 <=> 236.33/34.79 (![A,Xx,B]: (subset(A,B) => subset(A,setadjoin(Xx,B))))). 236.33/34.79 tff('74', plain, 236.33/34.79 setadjoinSub2 = 236.33/34.79 (![X4,X6,X8]: (subset(X4,X8) => subset(X4,setadjoin(X6,X8)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setadjoinSub, axiom, setadjoinSub <=> 236.33/34.79 (![Xx,A]: subset(A,setadjoin(Xx,A)))). 236.33/34.79 tff('75', plain, setadjoinSub = (![X4,X6]: subset(X6,setadjoin(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subsetTrans, axiom, subsetTrans <=> 236.33/34.79 (![A,B,C]: (subset(A,B) => (subset(B,C) => subset(A,C))))). 236.33/34.79 tff('76', plain, 236.33/34.79 subsetTrans = 236.33/34.79 (![X4,X6,X8]: (subset(X4,X6) => (subset(X6,X8) => subset(X4,X8)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subsetRefl, axiom, subsetRefl <=> (![A]: subset(A,A))). 236.33/34.79 tff('77', plain, subsetRefl = (![X4]: subset(X4,X4)), define([status(thm)])). 236.33/34.79 tff(notequalI2, axiom, notequalI2 <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (A != B))))). 236.33/34.79 tff('78', plain, 236.33/34.79 notequalI2 = (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (X4 != X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(notequalI1, axiom, notequalI1 <=> (![A,B]: ((~subset(A,B)) => (A != B)))). 236.33/34.79 tff('79', plain, notequalI1 = (![X4,X6]: ((~subset(X4,X6)) => (X4 != X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(notsubsetI, axiom, notsubsetI <=> 236.33/34.79 (![A,B,Xx]: (in(Xx,A) => ((~in(Xx,B)) => (~subset(A,B)))))). 236.33/34.79 tff('80', plain, 236.33/34.79 notsubsetI = 236.33/34.79 (![X4,X6,X8]: (in(X8,X4) => ((~in(X8,X6)) => (~subset(X4,X6))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subsetE2, axiom, subsetE2 <=> 236.33/34.79 (![A,B,Xx]: (subset(A,B) => ((~in(Xx,B)) => (~in(Xx,A)))))). 236.33/34.79 tff('81', plain, 236.33/34.79 subsetE2 = 236.33/34.79 (![X4,X6,X8]: (subset(X4,X6) => ((~in(X8,X6)) => (~in(X8,X4))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subsetE, axiom, subsetE <=> 236.33/34.79 (![A,B,Xx]: (subset(A,B) => (in(Xx,A) => in(Xx,B))))). 236.33/34.79 tff('82', plain, 236.33/34.79 subsetE = (![X4,X6,X8]: (subset(X4,X6) => (in(X8,X4) => in(X8,X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(emptysetsubset, axiom, emptysetsubset <=> (![A]: subset(emptyset,A))). 236.33/34.79 tff('83', plain, emptysetsubset = (![X4]: subset(emptyset,X4)), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subsetI2, axiom, subsetI2 <=> 236.33/34.79 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 236.33/34.79 tff('84', plain, 236.33/34.79 subsetI2 = 236.33/34.79 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(eqimpsubset1, axiom, eqimpsubset1 <=> (![A,B]: ((A = B) => subset(A,B)))). 236.33/34.79 tff('85', plain, eqimpsubset1 = (![X4,X6]: ((X4 = X6) => subset(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(eqimpsubset2, axiom, eqimpsubset2 <=> (![A,B]: ((A = B) => subset(B,A)))). 236.33/34.79 tff('86', plain, eqimpsubset2 = (![X4,X6]: ((X4 = X6) => subset(X6,X4))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(subsetI1, axiom, subsetI1 <=> 236.33/34.79 (![A,B]: ((![Xx]: (in(Xx,A) => in(Xx,B))) => subset(A,B)))). 236.33/34.79 tff('87', plain, 236.33/34.79 subsetI1 = 236.33/34.79 (![X4,X6]: ((![X8]: (in(X8,X4) => in(X8,X6))) => subset(X4,X6))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(dsetconstr__Cong, axiom, dsetconstr__Cong <=> 236.33/34.79 (![A,B]: 236.33/34.79 ((A = B) => 236.33/34.79 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 236.33/34.79 ((![Xx]: 236.33/34.79 (in(Xx,A) => 236.33/34.79 (![Xy]: (in(Xy,B) => ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy))))))) => 236.33/34.79 (dsetconstr(A,^[Xx]: Xphi(Xx)) = dsetconstr(B,^[Xx]: Xpsi(Xx)))))))). 236.33/34.79 tff('88', plain, 236.33/34.79 dsetconstr__Cong = 236.33/34.79 (![X4,X6]: 236.33/34.79 ((X4 = X6) => 236.33/34.79 (![X8:(($i > $o)),X10:(($i > $o))]: 236.33/34.79 ((![X12]: 236.33/34.79 (in(X12,X4) => 236.33/34.79 (![X14]: 236.33/34.79 (in(X14,X6) => ((X12 = X14) => (X8(X12) <=> X10(X14))))))) => 236.33/34.79 (dsetconstr(X4,^[V_1]: X8(V_1)) = dsetconstr(X6,^[V_2]: X10(V_2))))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(descr__Cong, axiom, descr__Cong <=> 236.33/34.79 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 236.33/34.79 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 236.33/34.79 (exu(^[Xx]: Xphi(Xx)) => 236.33/34.79 (exu(^[Xx]: Xpsi(Xx)) => 236.33/34.79 (descr(^[Xx]: Xphi(Xx)) = descr(^[Xx]: Xpsi(Xx)))))))). 236.33/34.79 tff('89', plain, 236.33/34.79 descr__Cong = 236.33/34.79 (![X4:(($i > $o)),X6:(($i > $o))]: 236.33/34.79 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 236.33/34.79 (exu(^[V_1]: X4(V_1)) => 236.33/34.79 (exu(^[V_2]: X6(V_2)) => 236.33/34.79 (descr(^[V_3]: X4(V_3)) = descr(^[V_4]: X6(V_4))))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(exuEu, axiom, exuEu <=> 236.33/34.79 (![Xphi:(($i > $o))]: 236.33/34.79 (exu(^[Xx]: Xphi(Xx)) => 236.33/34.79 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 236.33/34.79 tff('90', plain, 236.33/34.79 exuEu = 236.33/34.79 (![X4:(($i > $o))]: 236.33/34.79 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(omega__Cong, axiom, omega__Cong <=> (omega = omega)). 236.33/34.79 tff('91', plain, omega__Cong = (omega = omega), define([status(thm)])). 236.33/34.79 tff(setunion__Cong, axiom, setunion__Cong <=> 236.33/34.79 (![A,B]: ((A = B) => (setunion(A) = setunion(B))))). 236.33/34.79 tff('92', plain, 236.33/34.79 setunion__Cong = (![X4,X6]: ((X4 = X6) => (setunion(X4) = setunion(X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(powerset__Cong, axiom, powerset__Cong <=> 236.33/34.79 (![A,B]: ((A = B) => (powerset(A) = powerset(B))))). 236.33/34.79 tff('93', plain, 236.33/34.79 powerset__Cong = (![X4,X6]: ((X4 = X6) => (powerset(X4) = powerset(X6)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(setadjoin__Cong, axiom, setadjoin__Cong <=> 236.33/34.79 (![Xx,Xy]: 236.33/34.79 ((Xx = Xy) => 236.33/34.79 (![Xz,Xu]: ((Xz = Xu) => (setadjoin(Xx,Xz) = setadjoin(Xy,Xu))))))). 236.33/34.79 tff('94', plain, 236.33/34.79 setadjoin__Cong = 236.33/34.79 (![X4,X6]: 236.33/34.79 ((X4 = X6) => 236.33/34.79 (![X8,X10]: ((X8 = X10) => (setadjoin(X4,X8) = setadjoin(X6,X10)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(emptyset__Cong, axiom, emptyset__Cong <=> (emptyset = emptyset)). 236.33/34.79 tff('95', plain, emptyset__Cong = (emptyset = emptyset), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(exu__Cong, axiom, exu__Cong <=> 236.33/34.79 (![Xphi:(($i > $o)),Xpsi:(($i > $o))]: 236.33/34.79 ((![Xx,Xy]: ((Xx = Xy) => (Xphi(Xx) <=> Xpsi(Xy)))) => 236.33/34.79 (exu(^[Xx]: Xphi(Xx)) <=> exu(^[Xx]: Xpsi(Xx)))))). 236.33/34.79 tff('96', plain, 236.33/34.79 exu__Cong = 236.33/34.79 (![X4:(($i > $o)),X6:(($i > $o))]: 236.33/34.79 ((![X8,X10]: ((X8 = X10) => (X4(X8) <=> X6(X10)))) => 236.33/34.79 (exu(^[V_1]: X4(V_1)) <=> exu(^[V_2]: X6(V_2))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(exuE3u, axiom, exuE3u <=> 236.33/34.79 (![Xphi:(($i > $o))]: 236.33/34.79 (exu(^[Xx]: Xphi(Xx)) => 236.33/34.79 (![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy))))))). 236.33/34.79 tff('97', plain, 236.33/34.79 exuE3u = 236.33/34.79 (![X4:(($i > $o))]: 236.33/34.79 (exu(^[V_1]: X4(V_1)) => (![X6,X8]: (X4(X6) => (X4(X8) => (X6 = X8)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(in__Cong, axiom, in__Cong <=> 236.33/34.79 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) <=> in(Xy,B))))))). 236.33/34.79 tff('98', plain, 236.33/34.79 in__Cong = 236.33/34.79 (![X4,X6]: 236.33/34.79 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) <=> in(X10,X6)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(inCongP, axiom, inCongP <=> 236.33/34.79 (![A,B]: ((A = B) => (![Xx,Xy]: ((Xx = Xy) => (in(Xx,A) => in(Xy,B))))))). 236.33/34.79 tff('99', plain, 236.33/34.79 inCongP = 236.33/34.79 (![X4,X6]: 236.33/34.79 ((X4 = X6) => (![X8,X10]: ((X8 = X10) => (in(X8,X4) => in(X10,X6)))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(exuI2, axiom, exuI2 <=> 236.33/34.79 (![Xphi:(($i > $o))]: 236.33/34.79 ((?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx)))) => exu(^[Xx]: Xphi(Xx))))). 236.33/34.79 tff('100', plain, 236.33/34.79 exuI2 = 236.33/34.79 (![X4:(($i > $o))]: 236.33/34.79 ((?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))) => exu(^[V_1]: X4(V_1)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(exuI3, axiom, exuI3 <=> 236.33/34.79 (![Xphi:(($i > $o))]: 236.33/34.79 ((?[Xx]: Xphi(Xx)) => 236.33/34.79 ((![Xx,Xy]: (Xphi(Xx) => (Xphi(Xy) => (Xx = Xy)))) => 236.33/34.79 exu(^[Xx]: Xphi(Xx)))))). 236.33/34.79 tff('101', plain, 236.33/34.79 exuI3 = 236.33/34.79 (![X4:(($i > $o))]: 236.33/34.79 ((?[X6]: X4(X6)) => 236.33/34.79 ((![X8,X10]: (X4(X8) => (X4(X10) => (X8 = X10)))) => 236.33/34.79 exu(^[V_1]: X4(V_1))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(exuI1, axiom, exuI1 <=> 236.33/34.79 (![Xphi:(($i > $o))]: 236.33/34.79 ((?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx))) => 236.33/34.79 exu(^[Xx]: Xphi(Xx))))). 236.33/34.79 tff('102', plain, 236.33/34.79 exuI1 = 236.33/34.79 (![X4:(($i > $o))]: 236.33/34.79 ((?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))) => 236.33/34.79 exu(^[V_1]: X4(V_1)))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(notdallE, axiom, notdallE <=> 236.33/34.79 (![A,Xphi:(($i > $o))]: 236.33/34.79 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 236.33/34.79 tff('103', plain, 236.33/34.79 notdallE = 236.33/34.79 (![X4,X6:(($i > $o))]: 236.33/34.79 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 236.33/34.79 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 236.33/34.79 define([status(thm)])). 236.33/34.79 tff(notdexE, axiom, notdexE <=> 236.33/34.79 (![A,Xphi:(($i > $o))]: 236.33/34.79 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 236.33/34.80 tff('104', plain, 236.33/34.80 notdexE = 236.33/34.80 (![X4,X6:(($i > $o))]: 236.33/34.80 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 236.33/34.80 (![X10]: (in(X10,X4) => (~X6(X10)))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(prop2set2propI, axiom, prop2set2propI <=> 236.33/34.80 (![Xphi:$o]: (Xphi => set2prop(prop2set(Xphi))))). 236.33/34.80 tff('105', plain, 236.33/34.80 prop2set2propI = (![X4:$o]: (X4 => set2prop(prop2set(X4)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(prop2setI, axiom, prop2setI <=> 236.33/34.80 (![Xphi:$o]: (Xphi => in(emptyset,prop2set(Xphi))))). 236.33/34.80 tff('106', plain, prop2setI = (![X4:$o]: (X4 => in(emptyset,prop2set(X4)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(quantDeMorgan4, axiom, quantDeMorgan4 <=> 236.33/34.80 (![A,Xphi:(($i > $o))]: 236.33/34.80 ((?[Xx]: ((~Xphi(Xx)) & in(Xx,A))) => (~(![Xx]: (in(Xx,A) => Xphi(Xx))))))). 236.33/34.80 tff('107', plain, 236.33/34.80 quantDeMorgan4 = 236.33/34.80 (![X4,X6:(($i > $o))]: 236.33/34.80 ((?[X8]: ((~X6(X8)) & in(X8,X4))) => 236.33/34.80 (~(![X10]: (in(X10,X4) => X6(X10)))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(quantDeMorgan3, axiom, quantDeMorgan3 <=> 236.33/34.80 (![A,Xphi:(($i > $o))]: 236.33/34.80 ((~(?[Xx]: (Xphi(Xx) & in(Xx,A)))) => (![Xx]: (in(Xx,A) => (~Xphi(Xx))))))). 236.33/34.80 tff('108', plain, 236.33/34.80 quantDeMorgan3 = 236.33/34.80 (![X4,X6:(($i > $o))]: 236.33/34.80 ((~(?[X8]: (X6(X8) & in(X8,X4)))) => 236.33/34.80 (![X10]: (in(X10,X4) => (~X6(X10)))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(quantDeMorgan2, axiom, quantDeMorgan2 <=> 236.33/34.80 (![A,Xphi:(($i > $o))]: 236.33/34.80 ((![Xx]: (in(Xx,A) => (~Xphi(Xx)))) => (~(?[Xx]: (Xphi(Xx) & in(Xx,A))))))). 236.33/34.80 tff('109', plain, 236.33/34.80 quantDeMorgan2 = 236.33/34.80 (![X4,X6:(($i > $o))]: 236.33/34.80 ((![X8]: (in(X8,X4) => (~X6(X8)))) => 236.33/34.80 (~(?[X10]: (X6(X10) & in(X10,X4)))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(quantDeMorgan1, axiom, quantDeMorgan1 <=> 236.33/34.80 (![A,Xphi:(($i > $o))]: 236.33/34.80 ((~(![Xx]: (in(Xx,A) => Xphi(Xx)))) => (?[Xx]: ((~Xphi(Xx)) & in(Xx,A)))))). 236.33/34.80 tff('110', plain, 236.33/34.80 quantDeMorgan1 = 236.33/34.80 (![X4,X6:(($i > $o))]: 236.33/34.80 ((~(![X8]: (in(X8,X4) => X6(X8)))) => 236.33/34.80 (?[X10]: ((~X6(X10)) & in(X10,X4))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(vacuousDall, axiom, vacuousDall <=> 236.33/34.80 (![Xphi:(($i > $o)),Xx]: (in(Xx,emptyset) => Xphi(Xx)))). 236.33/34.80 tff('111', plain, 236.33/34.80 vacuousDall = (![X4:(($i > $o)),X6]: (in(X6,emptyset) => X4(X6))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptyE1, axiom, emptyE1 <=> 236.33/34.80 (![A,Xphi:(($i > $o))]: 236.33/34.80 ((?[Xx]: (Xphi(Xx) & in(Xx,A))) => 236.33/34.80 ((dsetconstr(A,^[Xx]: Xphi(Xx)) = emptyset) => $false)))). 236.33/34.80 tff('112', plain, 236.33/34.80 emptyE1 = 236.33/34.80 (![X4,X6:(($i > $o))]: 236.33/34.80 ((?[X8]: (X6(X8) & in(X8,X4))) => 236.33/34.80 ((dsetconstr(X4,^[V_1]: X6(V_1)) = emptyset) => $false))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(upairsetIR, axiom, upairsetIR <=> 236.33/34.80 (![Xx,Xy]: in(Xy,setadjoin(Xx,setadjoin(Xy,emptyset))))). 236.33/34.80 tff('113', plain, 236.33/34.80 upairsetIR = (![X4,X6]: in(X6,setadjoin(X4,setadjoin(X6,emptyset)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(upairsetIL, axiom, upairsetIL <=> 236.33/34.80 (![Xx,Xy]: in(Xx,setadjoin(Xx,setadjoin(Xy,emptyset))))). 236.33/34.80 tff('114', plain, 236.33/34.80 upairsetIL = (![X4,X6]: in(X4,setadjoin(X4,setadjoin(X6,emptyset)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(upairsetE, axiom, upairsetE <=> 236.33/34.80 (![Xx,Xy,Xz]: 236.33/34.80 (in(Xz,setadjoin(Xx,setadjoin(Xy,emptyset))) => ((Xz = Xx) | (Xz = Xy))))). 236.33/34.80 tff('115', plain, 236.33/34.80 upairsetE = 236.33/34.80 (![X4,X6,X8]: 236.33/34.80 (in(X8,setadjoin(X4,setadjoin(X6,emptyset))) => 236.33/34.80 ((X8 = X4) | (X8 = X6)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(singletonsswitch, axiom, singletonsswitch <=> 236.33/34.80 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => in(Xy,setadjoin(Xx,emptyset))))). 236.33/34.80 tff('116', plain, 236.33/34.80 singletonsswitch = 236.33/34.80 (![X4,X6]: 236.33/34.80 (in(X4,setadjoin(X6,emptyset)) => in(X6,setadjoin(X4,emptyset)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(eqinunit, axiom, eqinunit <=> 236.33/34.80 (![Xx,Xy]: ((Xx = Xy) => in(Xx,setadjoin(Xy,emptyset))))). 236.33/34.80 tff('117', plain, 236.33/34.80 eqinunit = (![X4,X6]: ((X4 = X6) => in(X4,setadjoin(X6,emptyset)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(notinsingleton, axiom, notinsingleton <=> 236.33/34.80 (![Xx,Xy]: ((Xx != Xy) => (~in(Xy,setadjoin(Xx,emptyset)))))). 236.33/34.80 tff('118', plain, 236.33/34.80 notinsingleton = 236.33/34.80 (![X4,X6]: ((X4 != X6) => (~in(X6,setadjoin(X4,emptyset))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(uniqinunit, axiom, uniqinunit <=> 236.33/34.80 (![Xx,Xy]: (in(Xx,setadjoin(Xy,emptyset)) => (Xx = Xy)))). 236.33/34.80 tff('119', plain, 236.33/34.80 uniqinunit = (![X4,X6]: (in(X4,setadjoin(X6,emptyset)) => (X4 = X6))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(nonemptyImpWitness, axiom, nonemptyImpWitness <=> 236.33/34.80 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 236.33/34.80 tff('120', plain, 236.33/34.80 nonemptyImpWitness = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(exuE2, axiom, exuE2 <=> 236.33/34.80 (![Xphi:(($i > $o))]: 236.33/34.80 (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: (![Xy]: (Xphi(Xy) <=> (Xy = Xx))))))). 236.33/34.80 tff('121', plain, 236.33/34.80 exuE2 = 236.33/34.80 (![X4:(($i > $o))]: 236.33/34.80 (exu(^[V_1]: X4(V_1)) => (?[X6]: (![X8]: (X4(X8) <=> (X8 = X6)))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(subPowSU, axiom, subPowSU <=> 236.33/34.80 (![A,Xx]: (in(Xx,A) => in(Xx,powerset(setunion(A)))))). 236.33/34.80 tff('122', plain, 236.33/34.80 subPowSU = (![X4,X6]: (in(X6,X4) => in(X6,powerset(setunion(X4))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setunionE, axiom, setunionE <=> 236.33/34.80 (![A,Xx]: 236.33/34.80 (in(Xx,setunion(A)) => 236.33/34.80 (![Xphi:$o]: ((![B]: (in(Xx,B) => (in(B,A) => Xphi))) => Xphi))))). 236.33/34.80 tff('123', plain, 236.33/34.80 setunionE = 236.33/34.80 (![X4,X6]: 236.33/34.80 (in(X6,setunion(X4)) => 236.33/34.80 (![X8:$o]: ((![X10]: (in(X6,X10) => (in(X10,X4) => X8))) => X8)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setunionI, axiom, setunionI <=> 236.33/34.80 (![A,Xx,B]: (in(Xx,B) => (in(B,A) => in(Xx,setunion(A)))))). 236.33/34.80 tff('124', plain, 236.33/34.80 setunionI = 236.33/34.80 (![X4,X6,X8]: (in(X6,X8) => (in(X8,X4) => in(X6,setunion(X4))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(powersetE, axiom, powersetE <=> 236.33/34.80 (![A,B,Xx]: (in(B,powerset(A)) => (in(Xx,B) => in(Xx,A))))). 236.33/34.80 tff('125', plain, 236.33/34.80 powersetE = 236.33/34.80 (![X4,X6,X8]: (in(X6,powerset(X4)) => (in(X8,X6) => in(X8,X4)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptyInPowerset, axiom, emptyInPowerset <=> 236.33/34.80 (![A]: in(emptyset,powerset(A)))). 236.33/34.80 tff('126', plain, emptyInPowerset = (![X4]: in(emptyset,powerset(X4))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptyinPowerset, axiom, emptyinPowerset <=> 236.33/34.80 (![A]: in(emptyset,powerset(A)))). 236.33/34.80 tff('127', plain, emptyinPowerset = (![X4]: in(emptyset,powerset(X4))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(powersetI, axiom, powersetI <=> 236.33/34.80 (![A,B]: ((![Xx]: (in(Xx,B) => in(Xx,A))) => in(B,powerset(A))))). 236.33/34.80 tff('128', plain, 236.33/34.80 powersetI = 236.33/34.80 (![X4,X6]: ((![X8]: (in(X8,X6) => in(X8,X4))) => in(X6,powerset(X4)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setoftrueEq, axiom, setoftrueEq <=> 236.33/34.80 (![A]: (dsetconstr(A,^[Xx]: $true) = A))). 236.33/34.80 tff('129', plain, setoftrueEq = (![X4]: (dsetconstr(X4,^[V_1]: $true) = X4)), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setadjoinOr, axiom, setadjoinOr <=> 236.33/34.80 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) => ((Xy = Xx) | in(Xy,A))))). 236.33/34.80 tff('130', plain, 236.33/34.80 setadjoinOr = 236.33/34.80 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) => ((X8 = X4) | in(X8,X6)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setadjoinE, axiom, setadjoinE <=> 236.33/34.80 (![Xx,A,Xy]: 236.33/34.80 (in(Xy,setadjoin(Xx,A)) => 236.33/34.80 (![Xphi:$o]: (((Xy = Xx) => Xphi) => ((in(Xy,A) => Xphi) => Xphi)))))). 236.33/34.80 tff('131', plain, 236.33/34.80 setadjoinE = 236.33/34.80 (![X4,X6,X8]: 236.33/34.80 (in(X8,setadjoin(X4,X6)) => 236.33/34.80 (![X10:$o]: (((X8 = X4) => X10) => ((in(X8,X6) => X10) => X10))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setadjoinIR, axiom, setadjoinIR <=> 236.33/34.80 (![Xx,A,Xy]: (in(Xy,A) => in(Xy,setadjoin(Xx,A))))). 236.33/34.80 tff('132', plain, 236.33/34.80 setadjoinIR = (![X4,X6,X8]: (in(X8,X6) => in(X8,setadjoin(X4,X6)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptyinunitempty, axiom, emptyinunitempty() = 236.33/34.80 in(emptyset,setadjoin(emptyset,emptyset))). 236.33/34.80 tff('133', plain, 236.33/34.80 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 236.33/34.80 inference('simplify_rw_rule', [status(thm)], [emptyinunitempty])). 236.33/34.80 tff('134', plain, 236.33/34.80 emptyinunitempty = in(emptyset,setadjoin(emptyset,emptyset)), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setadjoinIL, axiom, setadjoinIL <=> (![Xx,Xy]: in(Xx,setadjoin(Xx,Xy)))). 236.33/34.80 tff('135', plain, setadjoinIL = (![X4,X6]: in(X4,setadjoin(X4,X6))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(nonemptyI1, axiom, nonemptyI1 <=> 236.33/34.80 (![A]: ((?[Xx]: in(Xx,A)) => nonempty(A)))). 236.33/34.80 tff('136', plain, nonemptyI1 = (![X4]: ((?[X6]: in(X6,X4)) => nonempty(X4))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(nonemptyI, axiom, nonemptyI <=> 236.33/34.80 (![A,Xphi:(($i > $o)),Xx]: 236.33/34.80 (in(Xx,A) => (Xphi(Xx) => nonempty(dsetconstr(A,^[Xy]: Xphi(Xy))))))). 236.33/34.80 tff('137', plain, 236.33/34.80 nonemptyI = 236.33/34.80 (![X4,X6:(($i > $o)),X8]: 236.33/34.80 (in(X8,X4) => (X6(X8) => nonempty(dsetconstr(X4,^[V_1]: X6(V_1)))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(nonemptyE1, axiom, nonemptyE1 <=> 236.33/34.80 (![A]: (nonempty(A) => (?[Xx]: in(Xx,A))))). 236.33/34.80 tff('138', plain, nonemptyE1 = (![X4]: (nonempty(X4) => (?[X6]: in(X6,X4)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(nonempty, axiom, nonempty() = ^[Xx]: (Xx != emptyset)). 236.33/34.80 tff('139', plain, nonempty = (^[Xx]: (Xx != emptyset)), 236.33/34.80 inference('simplify_rw_rule', [status(thm)], [nonempty])). 236.33/34.80 tff('140', plain, nonempty = (^[V_1]: (V_1 != emptyset)), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setbeta, axiom, setbeta <=> 236.33/34.80 (![A,Xphi:(($i > $o)),Xx]: 236.33/34.80 (in(Xx,A) => (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) <=> Xphi(Xx))))). 236.33/34.80 tff('141', plain, 236.33/34.80 setbeta = 236.33/34.80 (![X4,X6:(($i > $o)),X8]: 236.33/34.80 (in(X8,X4) => (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) <=> X6(X8)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(noeltsimpempty, axiom, noeltsimpempty <=> 236.33/34.80 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 236.33/34.80 tff('142', plain, 236.33/34.80 noeltsimpempty = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptyI, axiom, emptyI <=> 236.33/34.80 (![A]: ((![Xx]: (~in(Xx,A))) => (A = emptyset)))). 236.33/34.80 tff('143', plain, 236.33/34.80 emptyI = (![X4]: ((![X6]: (~in(X6,X4))) => (X4 = emptyset))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setext, axiom, setext <=> 236.33/34.80 (![A,B]: 236.33/34.80 ((![Xx]: (in(Xx,A) => in(Xx,B))) => 236.33/34.80 ((![Xx]: (in(Xx,B) => in(Xx,A))) => (A = B))))). 236.33/34.80 tff('144', plain, 236.33/34.80 setext = 236.33/34.80 (![X4,X6]: 236.33/34.80 ((![X8]: (in(X8,X4) => in(X8,X6))) => 236.33/34.80 ((![X10]: (in(X10,X6) => in(X10,X4))) => (X4 = X6)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(exuE3e, axiom, exuE3e <=> 236.33/34.80 (![Xphi:(($i > $o))]: (exu(^[Xx]: Xphi(Xx)) => (?[Xx]: Xphi(Xx))))). 236.33/34.80 tff('145', plain, 236.33/34.80 exuE3e = (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => (?[X6]: X4(X6)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(notinemptyset, axiom, notinemptyset <=> (![Xx]: (~in(Xx,emptyset)))). 236.33/34.80 tff('146', plain, notinemptyset = (![X4]: (~in(X4,emptyset))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptysetimpfalse, axiom, emptysetimpfalse <=> 236.33/34.80 (![Xx]: (in(Xx,emptyset) => $false))). 236.33/34.80 tff('147', plain, emptysetimpfalse = (![X4]: (in(X4,emptyset) => $false)), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptysetE, axiom, emptysetE <=> 236.33/34.80 (![Xx]: (in(Xx,emptyset) => (![Xphi:$o]: Xphi)))). 236.33/34.80 tff('148', plain, emptysetE = (![X4]: (in(X4,emptyset) => (![X6:$o]: X6))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(prop2setE, axiom, prop2setE <=> 236.33/34.80 (![Xphi:$o,Xx]: (in(Xx,prop2set(Xphi)) => Xphi))). 236.33/34.80 tff('149', plain, prop2setE = (![X4:$o,X6]: (in(X6,prop2set(X4)) => X4)), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(exuE1, axiom, exuE1 <=> 236.33/34.80 (![Xphi:(($i > $o))]: 236.33/34.80 (exu(^[Xx]: Xphi(Xx)) => 236.33/34.80 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))))). 236.33/34.80 tff('150', plain, 236.33/34.80 exuE1 = 236.33/34.80 (![X4:(($i > $o))]: 236.33/34.80 (exu(^[V_1]: X4(V_1)) => 236.33/34.80 (?[X6]: ((![X8]: (X4(X8) => (X6 = X8))) & X4(X6))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(dsetconstrER, axiom, dsetconstrER <=> 236.33/34.80 (![A,Xphi:(($i > $o)),Xx]: 236.33/34.80 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => Xphi(Xx)))). 236.33/34.80 tff('151', plain, 236.33/34.80 dsetconstrER = 236.33/34.80 (![X4,X6:(($i > $o)),X8]: 236.33/34.80 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => X6(X8))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(dsetconstrEL, axiom, dsetconstrEL <=> 236.33/34.80 (![A,Xphi:(($i > $o)),Xx]: 236.33/34.80 (in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))) => in(Xx,A)))). 236.33/34.80 tff('152', plain, 236.33/34.80 dsetconstrEL = 236.33/34.80 (![X4,X6:(($i > $o)),X8]: 236.33/34.80 (in(X8,dsetconstr(X4,^[V_1]: X6(V_1))) => in(X8,X4))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(dsetconstrI, axiom, dsetconstrI <=> 236.33/34.80 (![A,Xphi:(($i > $o)),Xx]: 236.33/34.80 (in(Xx,A) => (Xphi(Xx) => in(Xx,dsetconstr(A,^[Xy]: Xphi(Xy))))))). 236.33/34.80 tff('153', plain, 236.33/34.80 dsetconstrI = 236.33/34.80 (![X4,X6:(($i > $o)),X8]: 236.33/34.80 (in(X8,X4) => (X6(X8) => in(X8,dsetconstr(X4,^[V_1]: X6(V_1)))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(descrp, axiom, descrp <=> 236.33/34.80 (![Xphi:(($i > $o))]: 236.33/34.80 (exu(^[Xx]: Xphi(Xx)) => Xphi(descr(^[Xx]: Xphi(Xx)))))). 236.33/34.80 tff('154', plain, 236.33/34.80 descrp = 236.33/34.80 (![X4:(($i > $o))]: (exu(^[V_1]: X4(V_1)) => X4(descr(^[V_2]: X4(V_2))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(wellorderingAx, axiom, wellorderingAx <=> 236.33/34.80 (![A]: 236.33/34.80 (?[B]: 236.33/34.80 ((![C]: 236.33/34.80 (((![Xx]: (in(Xx,C) => in(Xx,A))) & (?[Xx]: in(Xx,C))) => 236.33/34.80 (?[D,Xx]: 236.33/34.80 ((![E]: 236.33/34.80 (in(E,B) => ((![Xy]: (in(Xy,E) => in(Xy,D))) | in(Xx,E)))) & 236.33/34.80 (~(?[Xy]: (in(Xy,C) & in(Xy,D)))) & in(Xx,C) & in(D,B))))) & 236.33/34.80 (![C,D]: 236.33/34.80 ((in(C,B) & in(D,B)) => 236.33/34.80 ((![Xx]: (in(Xx,C) => in(Xx,D))) | 236.33/34.80 (![Xx]: (in(Xx,D) => in(Xx,C)))))) & 236.33/34.80 (![Xx,Xy]: 236.33/34.80 ((in(Xx,A) & in(Xy,A)) => 236.33/34.80 ((![C]: (in(C,B) => (in(Xx,C) <=> in(Xy,C)))) => (Xx = Xy)))) & 236.33/34.80 (![C]: (in(C,B) => (![Xx]: (in(Xx,C) => in(Xx,A))))))))). 236.33/34.80 tff('155', plain, 236.33/34.80 wellorderingAx = 236.33/34.80 (![X4]: 236.33/34.80 (?[X6]: 236.33/34.80 ((![X8]: 236.33/34.80 (((![X10]: (in(X10,X8) => in(X10,X4))) & (?[X12]: in(X12,X8))) => 236.33/34.80 (?[X14,X16]: 236.33/34.80 ((![X18]: 236.33/34.80 (in(X18,X6) => 236.33/34.80 ((![X20]: (in(X20,X18) => in(X20,X14))) | in(X16,X18)))) & 236.33/34.80 (~(?[X22]: (in(X22,X8) & in(X22,X14)))) & in(X16,X8) & 236.33/34.80 in(X14,X6))))) & 236.33/34.80 (![X24,X26]: 236.33/34.80 ((in(X24,X6) & in(X26,X6)) => 236.33/34.80 ((![X28]: (in(X28,X24) => in(X28,X26))) | 236.33/34.80 (![X30]: (in(X30,X26) => in(X30,X24)))))) & 236.33/34.80 (![X32,X34]: 236.33/34.80 ((in(X32,X4) & in(X34,X4)) => 236.33/34.80 ((![X36]: (in(X36,X6) => (in(X32,X36) <=> in(X34,X36)))) => 236.33/34.80 (X32 = X34)))) & 236.33/34.80 (![X38]: (in(X38,X6) => (![X40]: (in(X40,X38) => in(X40,X4)))))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(foundationAx, axiom, foundationAx <=> 236.33/34.80 (![A]: 236.33/34.80 ((?[Xx]: in(Xx,A)) => 236.33/34.80 (?[B]: ((~(?[Xx]: (in(Xx,A) & in(Xx,B)))) & in(B,A)))))). 236.33/34.80 tff('156', plain, 236.33/34.80 foundationAx = 236.33/34.80 (![X4]: 236.33/34.80 ((?[X6]: in(X6,X4)) => 236.33/34.80 (?[X8]: ((~(?[X10]: (in(X10,X4) & in(X10,X8)))) & in(X8,X4))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(replAx, axiom, replAx <=> 236.33/34.80 (![Xphi:(($i * $i) > $o),A]: 236.33/34.80 ((![Xx]: (in(Xx,A) => exu(^[Xy]: Xphi(Xx,Xy)))) => 236.33/34.80 (?[B]: (![Xx]: (in(Xx,B) <=> (?[Xy]: (Xphi(Xy,Xx) & in(Xy,A))))))))). 236.33/34.80 tff('157', plain, 236.33/34.80 replAx = 236.33/34.80 (![X4:(($i * $i) > $o),X6]: 236.33/34.80 ((![X8]: (in(X8,X6) => exu(^[V_1]: X4(X8,V_1)))) => 236.33/34.80 (?[X10]: 236.33/34.80 (![X12]: (in(X12,X10) <=> (?[X14]: (X4(X14,X12) & in(X14,X6)))))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(omegaIndAx, axiom, omegaIndAx <=> 236.33/34.80 (![A]: 236.33/34.80 ((in(emptyset,A) & 236.33/34.80 (![Xx]: ((in(Xx,omega) & in(Xx,A)) => in(setadjoin(Xx,Xx),A)))) => 236.33/34.80 (![Xx]: (in(Xx,omega) => in(Xx,A)))))). 236.33/34.80 tff('158', plain, 236.33/34.80 omegaIndAx = 236.33/34.80 (![X4]: 236.33/34.80 ((in(emptyset,X4) & 236.33/34.80 (![X6]: ((in(X6,omega) & in(X6,X4)) => in(setadjoin(X6,X6),X4)))) => 236.33/34.80 (![X8]: (in(X8,omega) => in(X8,X4))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(omegaSAx, axiom, omegaSAx <=> 236.33/34.80 (![Xx]: (in(Xx,omega) => in(setadjoin(Xx,Xx),omega)))). 236.33/34.80 tff('159', plain, 236.33/34.80 omegaSAx = (![X4]: (in(X4,omega) => in(setadjoin(X4,X4),omega))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(omega0Ax, axiom, omega0Ax() = in(emptyset,omega)). 236.33/34.80 tff('160', plain, omega0Ax = in(emptyset,omega), 236.33/34.80 inference('simplify_rw_rule', [status(thm)], [omega0Ax])). 236.33/34.80 tff('161', plain, omega0Ax = in(emptyset,omega), define([status(thm)])). 236.33/34.80 tff(setunionAx, axiom, setunionAx <=> 236.33/34.80 (![A,Xx]: (in(Xx,setunion(A)) <=> (?[B]: (in(B,A) & in(Xx,B)))))). 236.33/34.80 tff('162', plain, 236.33/34.80 setunionAx = 236.33/34.80 (![X4,X6]: (in(X6,setunion(X4)) <=> (?[X8]: (in(X8,X4) & in(X6,X8))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(powersetAx, axiom, powersetAx <=> 236.33/34.80 (![A,B]: (in(B,powerset(A)) <=> (![Xx]: (in(Xx,B) => in(Xx,A)))))). 236.33/34.80 tff('163', plain, 236.33/34.80 powersetAx = 236.33/34.80 (![X4,X6]: (in(X6,powerset(X4)) <=> (![X8]: (in(X8,X6) => in(X8,X4))))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setadjoinAx, axiom, setadjoinAx <=> 236.33/34.80 (![Xx,A,Xy]: (in(Xy,setadjoin(Xx,A)) <=> ((Xy = Xx) | in(Xy,A))))). 236.33/34.80 tff('164', plain, 236.33/34.80 setadjoinAx = 236.33/34.80 (![X4,X6,X8]: (in(X8,setadjoin(X4,X6)) <=> ((X8 = X4) | in(X8,X6)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(emptysetAx, axiom, emptysetAx <=> (![Xx]: (~in(Xx,emptyset)))). 236.33/34.80 tff('165', plain, emptysetAx = (![X4]: (~in(X4,emptyset))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(setextAx, axiom, setextAx <=> 236.33/34.80 (![A,B]: ((![Xx]: (in(Xx,A) <=> in(Xx,B))) => (A = B)))). 236.33/34.80 tff('166', plain, 236.33/34.80 setextAx = (![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(exu, axiom, exu() = 236.33/34.80 ^[Xphi:(($i > $o))]: (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))). 236.33/34.80 tff('167', plain, 236.33/34.80 exu = 236.33/34.80 (^[Xphi:(($i > $o))]: 236.33/34.80 (?[Xx]: ((![Xy]: (Xphi(Xy) => (Xx = Xy))) & Xphi(Xx)))), 236.33/34.80 inference('simplify_rw_rule', [status(thm)], [exu])). 236.33/34.80 tff('168', plain, 236.33/34.80 exu = 236.33/34.80 (^[V_1:(($i > $o))]: (?[X4]: ((![X6]: (V_1(X6) => (X4 = X6))) & V_1(X4)))), 236.33/34.80 define([status(thm)])). 236.33/34.80 tff(ex1I, conjecture, 236.33/34.80 (setextAx => 236.33/34.80 (emptysetAx => 236.33/34.80 (setadjoinAx => 236.33/34.80 (powersetAx => 236.33/34.80 (setunionAx => 236.33/34.80 (omega0Ax => 236.33/34.80 (omegaSAx => 236.33/34.80 (omegaIndAx => 236.33/34.80 (replAx => 236.33/34.80 (foundationAx => 236.33/34.80 (wellorderingAx => 236.33/34.80 (descrp => 236.33/34.80 (dsetconstrI => 236.33/34.80 (dsetconstrEL => 236.33/34.80 (dsetconstrER => 236.33/34.80 (exuE1 => 236.33/34.80 (prop2setE => 236.33/34.80 (emptysetE => 236.33/34.80 (emptysetimpfalse => 236.33/34.80 (notinemptyset => 236.33/34.80 (exuE3e => 236.33/34.80 (setext => 236.33/34.80 (emptyI => 236.33/34.80 (noeltsimpempty => 236.33/34.80 (setbeta => 236.33/34.80 (nonemptyE1 => 236.33/34.80 (nonemptyI => 236.33/34.80 (nonemptyI1 => 236.33/34.80 (setadjoinIL => 236.33/34.80 (emptyinunitempty => 236.33/34.80 (setadjoinIR => 236.33/34.80 (setadjoinE => 236.33/34.80 (setadjoinOr => 236.33/34.80 (setoftrueEq => 236.33/34.80 (powersetI => 236.33/34.80 (emptyinPowerset => 236.33/34.80 (emptyInPowerset => 236.33/34.80 (powersetE => 236.33/34.80 (setunionI => 236.33/34.80 (setunionE => 236.33/34.80 (subPowSU => 236.33/34.80 (exuE2 => 236.33/34.80 (nonemptyImpWitness => 236.33/34.80 (uniqinunit => 236.33/34.80 (notinsingleton => 236.33/34.80 (eqinunit => 236.33/34.80 (singletonsswitch => 236.33/34.80 (upairsetE => 236.33/34.80 (upairsetIL => 236.33/34.80 (upairsetIR => 236.33/34.80 (emptyE1 => 236.33/34.80 (vacuousDall => 236.33/34.80 (quantDeMorgan1 => 236.33/34.80 (quantDeMorgan2 => 236.33/34.80 (quantDeMorgan3 => 236.33/34.80 (quantDeMorgan4 => 236.33/34.80 (prop2setI => 236.33/34.80 (prop2set2propI => 236.33/34.80 (notdexE => 236.33/34.80 (notdallE => 236.33/34.80 (exuI1 => 236.33/34.80 (exuI3 => 236.33/34.80 (exuI2 => 236.33/34.80 (inCongP => 236.33/34.80 (in__Cong => 236.33/34.80 (exuE3u => 236.33/34.80 ( 236.33/34.80 exu__Cong => 236.33/34.80 ( 236.33/34.80 emptyset__Cong => 236.33/34.80 ( 236.33/34.80 setadjoin__Cong => 236.33/34.80 ( 236.33/34.80 powerset__Cong => 236.33/34.80 ( 236.33/34.80 setunion__Cong => 236.33/34.80 ( 236.33/34.80 omega__Cong => 236.33/34.80 ( 236.33/34.80 exuEu => 236.33/34.80 ( 236.33/34.80 descr__Cong => 236.33/34.80 ( 236.33/34.80 dsetconstr__Cong => 236.33/34.80 ( 236.33/34.80 subsetI1 => 236.33/34.80 ( 236.33/34.80 eqimpsubset2 => 236.33/34.80 ( 236.33/34.80 eqimpsubset1 => 236.33/34.80 ( 236.33/34.80 subsetI2 => 236.33/34.80 ( 236.33/34.80 emptysetsubset => 236.33/34.80 ( 236.33/34.80 subsetE => 236.33/34.80 ( 236.33/34.80 subsetE2 => 236.33/34.80 ( 236.33/34.80 notsubsetI => 236.33/34.80 ( 236.33/34.80 notequalI1 => 236.33/34.80 ( 236.33/34.80 notequalI2 => 236.33/34.80 ( 236.33/34.80 subsetRefl => 236.33/34.80 ( 236.33/34.80 subsetTrans => 236.33/34.80 ( 236.33/34.80 setadjoinSub => 236.33/34.80 ( 236.33/34.80 setadjoinSub2 => 236.33/34.80 ( 236.33/34.80 subset2powerset => 236.33/34.80 ( 236.33/34.80 setextsub => 236.33/34.80 ( 236.33/34.80 subsetemptysetimpeq => 236.33/34.80 ( 236.33/34.80 powersetI1 => 236.33/34.80 ( 236.33/34.80 powersetE1 => 236.33/34.80 ( 236.33/34.80 inPowerset => 236.33/34.80 ( 236.33/34.80 powersetsubset => 236.33/34.80 ( 236.33/34.80 sepInPowerset => 236.33/34.80 ( 236.33/34.80 sepSubset => 236.33/34.80 ( 236.33/34.80 binunionIL => 236.33/34.80 ( 236.33/34.80 upairset2IR => 236.33/34.80 ( 236.33/34.80 binunionIR => 236.33/34.80 ( 236.33/34.80 binunionEcases => 236.33/34.80 ( 236.33/34.80 binunionE => 236.33/34.80 ( 236.33/34.80 binunionLsub => 236.33/34.80 ( 236.33/34.80 binunionRsub => 236.33/34.80 ( 236.33/34.80 binintersectI => 236.33/34.80 ( 236.33/34.80 binintersectSubset5 => 236.33/34.80 ( 236.33/34.80 binintersectEL => 236.33/34.80 ( 236.33/34.80 binintersectLsub => 236.33/34.80 ( 236.33/34.80 binintersectSubset2 => 236.33/34.80 ( 236.33/34.80 binintersectSubset3 => 236.33/34.80 ( 236.33/34.80 binintersectER => 236.33/34.80 ( 236.33/34.80 disjointsetsI1 => 236.33/34.80 ( 236.33/34.80 binintersectRsub => 236.33/34.80 ( 236.33/34.80 binintersectSubset4 => 236.33/34.80 ( 236.33/34.80 binintersectSubset1 => 236.33/34.80 ( 236.33/34.80 bs114d => 236.33/34.80 ( 236.33/34.80 setminusI => 236.33/34.80 ( 236.33/34.80 setminusEL => 236.33/34.80 ( 236.33/34.80 setminusER => 236.33/34.80 ( 236.33/34.80 setminusSubset2 => 236.33/34.80 ( 236.33/34.80 setminusERneg => 236.33/34.80 ( 236.33/34.80 setminusELneg => 236.33/34.80 ( 236.33/34.80 setminusILneg => 236.33/34.80 ( 236.33/34.80 setminusIRneg => 236.33/34.80 ( 236.33/34.80 setminusLsub => 236.33/34.80 ( 236.33/34.80 setminusSubset1 => 236.33/34.80 ( 236.33/34.80 symdiffE => 236.33/34.80 ( 236.33/34.80 symdiffI1 => 236.33/34.80 ( 236.33/34.80 symdiffI2 => 236.33/34.80 ( 236.33/34.80 symdiffIneg1 => 236.33/34.80 ( 236.33/34.80 symdiffIneg2 => 236.33/34.80 ( 236.33/34.80 secondinupair => 236.33/34.80 ( 236.33/34.80 setukpairIL => 236.33/34.80 ( 236.33/34.80 setukpairIR => 236.33/34.80 ( 236.33/34.80 kpairiskpair => 236.33/34.80 ( 236.33/34.80 kpairp => 236.33/34.80 ( 236.33/34.80 singletonsubset => 236.33/34.80 ( 236.33/34.80 singletoninpowerset => 236.33/34.80 ( 236.33/34.80 singletoninpowunion => 236.33/34.80 ( 236.33/34.80 upairset2E => 236.33/34.80 ( 236.33/34.80 upairsubunion => 236.33/34.80 ( 236.33/34.80 upairinpowunion => 236.33/34.80 ( 236.33/34.80 ubforcartprodlem1 => 236.33/34.80 ( 236.33/34.80 ubforcartprodlem2 => 236.33/34.80 ( 236.33/34.80 ubforcartprodlem3 => 236.33/34.80 ( 236.33/34.80 cartprodpairin => 236.33/34.80 ( 236.33/34.80 cartprodmempair1 => 236.33/34.80 ( 236.33/34.80 cartprodmempair => 236.33/34.80 ( 236.33/34.80 setunionE2 => 236.33/34.80 ( 236.33/34.80 setunionsingleton1 => 236.33/34.80 ( 236.33/34.80 setunionsingleton2 => 236.33/34.80 ( 236.33/34.80 setunionsingleton => 236.33/34.80 ( 236.33/34.80 singletonprop => 236.33/34.80 ( 236.33/34.80 ex1E1 => 236.33/34.80 ( 236.33/34.80 ![A, 236.33/34.80 Xphi:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 Xx]: 236.33/34.80 (in(Xx,A) => 236.33/34.80 (Xphi(Xx) => 236.33/34.80 (( 236.33/34.80 ![Xy]: 236.33/34.80 (in(Xy,A) => 236.33/34.80 (Xphi(Xy) => 236.33/34.80 (Xy = Xx)))) => 236.33/34.80 ex1( 236.33/34.80 A, 236.33/34.80 ^[Xy]: 236.33/34.80 Xphi(Xy)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 236.33/34.80 tff(zf_stmt_0, conjecture, 236.33/34.80 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 236.33/34.80 ((![X10]: (~in(X10,emptyset))) => 236.33/34.80 ((![X12,X14,X16]: 236.33/34.80 (in(X16,setadjoin(X12,X14)) <=> (in(X16,X14) | (X16 = X12)))) => 236.33/34.80 ((![X18,X20]: 236.33/34.80 (in(X20,powerset(X18)) <=> (![X22]: (in(X22,X20) => in(X22,X18))))) => 236.33/34.80 ((![X24,X26]: 236.33/34.80 (in(X26,setunion(X24)) <=> (?[X28]: (in(X26,X28) & in(X28,X24))))) => 236.33/34.80 (in(emptyset,omega) => 236.33/34.80 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 236.33/34.80 ((![X32]: 236.33/34.80 (((![X34]: 236.33/34.80 ((in(X34,X32) & in(X34,omega)) => 236.33/34.80 in(setadjoin(X34,X34),X32))) & 236.33/34.80 in(emptyset,X32)) => 236.33/34.80 (![X36]: (in(X36,omega) => in(X36,X32))))) => 236.33/34.80 ((![X38:(($i * $i) > $o),X40]: 236.33/34.80 ((![X42]: 236.33/34.80 (in(X42,X40) => 236.33/34.80 (?[X44]: 236.33/34.80 (X38(X42,X44) & (![X46]: (X38(X42,X46) => (X44 = X46))))))) => 236.33/34.80 (?[X48]: 236.33/34.80 (![X50]: 236.33/34.80 (in(X50,X48) <=> (?[X52]: (in(X52,X40) & X38(X52,X50)))))))) => 236.33/34.80 ((![X54]: 236.33/34.80 ((?[X56]: in(X56,X54)) => 236.33/34.80 (?[X58]: 236.33/34.80 (in(X58,X54) & (~(?[X60]: (in(X60,X58) & in(X60,X54)))))))) => 236.33/34.80 ((![X62]: 236.33/34.80 (?[X64]: 236.33/34.80 ((![X96]: 236.33/34.80 (in(X96,X64) => (![X98]: (in(X98,X96) => in(X98,X62))))) & 236.33/34.80 (![X90,X92]: 236.33/34.80 ((in(X92,X62) & in(X90,X62)) => 236.33/34.80 ((![X94]: 236.33/34.80 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 236.33/34.80 (X90 = X92)))) & 236.33/34.80 (![X82,X84]: 236.33/34.80 ((in(X84,X64) & in(X82,X64)) => 236.33/34.80 ((![X88]: (in(X88,X84) => in(X88,X82))) | 236.33/34.80 (![X86]: (in(X86,X82) => in(X86,X84)))))) & 236.33/34.80 (![X66]: 236.33/34.80 (((?[X70]: in(X70,X66)) & 236.33/34.80 (![X68]: (in(X68,X66) => in(X68,X62)))) => 236.33/34.80 (?[X72,X74]: 236.33/34.80 (in(X72,X64) & in(X74,X66) & 236.33/34.80 (~(?[X80]: (in(X80,X72) & in(X80,X66)))) & 236.33/34.80 (![X76]: 236.33/34.80 (in(X76,X64) => 236.33/34.80 (in(X74,X76) | 236.33/34.80 (![X78]: (in(X78,X76) => in(X78,X72))))))))))))) => 236.33/34.80 ((![X100:(($i > $o))]: 236.33/34.80 ((?[X102]: 236.33/34.80 (X100(X102) & (![X104]: (X100(X104) => (X102 = X104))))) => 236.33/34.80 X100(descr(^[V_1]: X100(V_1))))) => 236.33/34.80 ((![X106,X108:(($i > $o)),X110]: 236.33/34.80 (in(X110,X106) => 236.33/34.80 (X108(X110) => in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 236.33/34.80 ((![X112,X114:(($i > $o)),X116]: 236.33/34.80 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 236.33/34.80 in(X116,X112))) => 236.33/34.80 ((![X118,X120:(($i > $o)),X122]: 236.33/34.80 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 236.33/34.80 X120(X122))) => 236.33/34.80 ((![X124:(($i > $o))]: 236.33/34.80 ((?[X126]: 236.33/34.80 (X124(X126) & 236.33/34.80 (![X128]: (X124(X128) => (X126 = X128))))) => 236.33/34.80 (?[X130]: 236.33/34.80 (X124(X130) & 236.33/34.80 (![X132]: (X124(X132) => (X130 = X132))))))) => 236.33/34.80 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 236.33/34.80 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 236.33/34.80 ((![X142]: (~in(X142,emptyset))) => 236.33/34.80 ((![X144]: (~in(X144,emptyset))) => 236.33/34.80 ((![X146:(($i > $o))]: 236.33/34.80 ((?[X148]: 236.33/34.80 (X146(X148) & 236.33/34.80 (![X150]: (X146(X150) => (X148 = X150))))) => 236.33/34.80 (?[X152]: X146(X152)))) => 236.33/34.80 ((![X154,X156]: 236.33/34.80 ((![X158]: (in(X158,X154) => in(X158,X156))) => 236.33/34.80 ((![X160]: (in(X160,X156) => in(X160,X154))) => 236.33/34.80 (X154 = X156)))) => 236.33/34.80 ((![X162]: 236.33/34.80 ((![X164]: (~in(X164,X162))) => (X162 = emptyset))) => 236.33/34.80 ((![X166]: 236.33/34.80 ((![X168]: (~in(X168,X166))) => 236.33/34.80 (X166 = emptyset))) => 236.33/34.80 ((![X170,X172:(($i > $o)),X174]: 236.33/34.80 (in(X174,X170) => 236.33/34.80 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 236.33/34.80 X172(X174)))) => 236.33/34.80 ((![X176]: 236.33/34.80 ((X176 != emptyset) => 236.33/34.80 (?[X178]: in(X178,X176)))) => 236.33/34.80 ((![X180,X182:(($i > $o)),X184]: 236.33/34.80 (in(X184,X180) => 236.33/34.80 (X182(X184) => 236.33/34.80 (dsetconstr(X180,^[V_6]: X182(V_6)) != 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X186]: 236.33/34.80 ((?[X188]: in(X188,X186)) => 236.33/34.80 (X186 != emptyset))) => 236.33/34.80 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 236.33/34.80 (in(emptyset,setadjoin(emptyset,emptyset)) => 236.33/34.80 ((![X194,X196,X198]: 236.33/34.80 (in(X198,X196) => 236.33/34.80 in(X198,setadjoin(X194,X196)))) => 236.33/34.80 ((![X200,X202,X204]: 236.33/34.80 (in(X204,setadjoin(X200,X202)) => 236.33/34.80 (![X206:$o]: 236.33/34.80 (((X204 = X200) => X206) => 236.33/34.80 ((in(X204,X202) => X206) => X206))))) => 236.33/34.80 ((![X208,X210,X212]: 236.33/34.80 (in(X212,setadjoin(X208,X210)) => 236.33/34.80 (in(X212,X210) | (X212 = X208)))) => 236.33/34.80 ((![X214]: 236.33/34.80 (dsetconstr(X214,^[V_7]: $true) = X214)) => 236.33/34.80 ((![X216,X218]: 236.33/34.80 ((![X220]: 236.33/34.80 (in(X220,X218) => in(X220,X216))) => 236.33/34.80 in(X218,powerset(X216)))) => 236.33/34.80 ((![X222]: in(emptyset,powerset(X222))) => 236.33/34.80 ((![X224]: in(emptyset,powerset(X224))) => 236.33/34.80 ((![X226,X228,X230]: 236.33/34.80 (in(X228,powerset(X226)) => 236.33/34.80 (in(X230,X228) => in(X230,X226)))) => 236.33/34.80 ((![X232,X234,X236]: 236.33/34.80 (in(X234,X236) => 236.33/34.80 (in(X236,X232) => 236.33/34.80 in(X234,setunion(X232))))) => 236.33/34.80 ((![X238,X240]: 236.33/34.80 (in(X240,setunion(X238)) => 236.33/34.80 (![X242:$o]: 236.33/34.80 ((![X244]: 236.33/34.80 (in(X240,X244) => 236.33/34.80 (in(X244,X238) => X242))) => 236.33/34.80 X242)))) => 236.33/34.80 ((![X246,X248]: 236.33/34.80 (in(X248,X246) => 236.33/34.80 in(X248, 236.33/34.80 powerset(setunion(X246))))) => 236.33/34.80 ((![X250:(($i > $o))]: 236.33/34.80 ((?[X252]: 236.33/34.80 (X250(X252) & 236.33/34.80 (![X254]: 236.33/34.80 (X250(X254) => 236.33/34.80 (X252 = X254))))) => 236.33/34.80 (?[X256]: 236.33/34.80 (![X258]: 236.33/34.80 (X250(X258) <=> 236.33/34.80 (X258 = X256)))))) => 236.33/34.80 ((![X260]: 236.33/34.80 ((X260 != emptyset) => 236.33/34.80 (?[X262]: in(X262,X260)))) => 236.33/34.80 ((![X264,X266]: 236.33/34.80 (in(X264, 236.33/34.80 setadjoin(X266,emptyset)) => 236.33/34.80 (X264 = X266))) => 236.33/34.80 ((![X268,X270]: 236.33/34.80 ((X268 != X270) => 236.33/34.80 (~ 236.33/34.80 in(X270, 236.33/34.80 setadjoin(X268, 236.33/34.80 emptyset))))) => 236.33/34.80 ((![X272,X274]: 236.33/34.80 ((X272 = X274) => 236.33/34.80 in(X272, 236.33/34.80 setadjoin(X274, 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X276,X278]: 236.33/34.80 (in(X276, 236.33/34.80 setadjoin(X278, 236.33/34.80 emptyset)) => 236.33/34.80 in(X278, 236.33/34.80 setadjoin(X276, 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X280,X282,X284]: 236.33/34.80 (in(X284, 236.33/34.80 setadjoin(X280, 236.33/34.80 setadjoin( 236.33/34.80 X282, 236.33/34.80 emptyset))) => 236.33/34.80 ((X284 = X282) | 236.33/34.80 (X284 = X280)))) => 236.33/34.80 ((![X286,X288]: 236.33/34.80 in(X286, 236.33/34.80 setadjoin(X286, 236.33/34.80 setadjoin( 236.33/34.80 X288, 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X290,X292]: 236.33/34.80 in(X292, 236.33/34.80 setadjoin(X290, 236.33/34.80 setadjoin( 236.33/34.80 X292, 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X294,X296:(($i > $o))]: 236.33/34.80 ((?[X298]: 236.33/34.80 (in(X298,X294) & 236.33/34.80 X296(X298))) => 236.33/34.80 (dsetconstr( 236.33/34.80 X294, 236.33/34.80 ^[V_8]: X296(V_8)) != 236.33/34.80 emptyset))) => 236.33/34.80 ((![X300:(($i > $o)), 236.33/34.80 X302]: 236.33/34.80 (in(X302,emptyset) => 236.33/34.80 X300(X302))) => 236.33/34.80 ((![X304, 236.33/34.80 X306:(($i > $o))]: 236.33/34.80 ((~ 236.33/34.80 (![X308]: 236.33/34.80 (in(X308,X304) => 236.33/34.80 X306(X308)))) => 236.33/34.80 (?[X310]: 236.33/34.80 (in(X310,X304) & 236.33/34.80 (~X306(X310)))))) => 236.33/34.80 ((![X312, 236.33/34.80 X314:(($i > $o))]: 236.33/34.80 ((![X316]: 236.33/34.80 (in(X316,X312) => 236.33/34.80 (~X314(X316)))) => 236.33/34.80 (~ 236.33/34.80 (?[X318]: 236.33/34.80 (in( 236.33/34.80 X318,X312) & 236.33/34.80 X314(X318)))))) => 236.33/34.80 ((![X320, 236.33/34.80 X322:(($i > $o))]: 236.33/34.80 ((~ 236.33/34.80 (?[X324]: 236.33/34.80 (in( 236.33/34.80 X324,X320) & 236.33/34.80 X322(X324)))) => 236.33/34.80 (![X326]: 236.33/34.80 (in(X326,X320) => 236.33/34.80 (~X322(X326)))))) => 236.33/34.80 ((![X328, 236.33/34.80 X330:(($i > $o))]: 236.33/34.80 ((?[X332]: 236.33/34.80 (in( 236.33/34.80 X332,X328) & 236.33/34.80 (~ 236.33/34.80 X330( 236.33/34.80 X332)))) => 236.33/34.80 (~ 236.33/34.80 (![X334]: 236.33/34.80 (in( 236.33/34.80 X334,X328) => 236.33/34.80 X330( 236.33/34.80 X334)))))) => 236.33/34.80 ((![X336:$o]: 236.33/34.80 (X336 => 236.33/34.80 in(emptyset, 236.33/34.80 prop2set( 236.33/34.80 X336)))) => 236.33/34.80 ((![X338:$o]: 236.33/34.80 (X338 => 236.33/34.80 set2prop( 236.33/34.80 prop2set( 236.33/34.80 X338)))) => 236.33/34.80 ((![X340, 236.33/34.80 X342:( 236.33/34.80 ($i > $o))]: 236.33/34.80 ((~ 236.33/34.80 (?[X344]: 236.33/34.80 (in( 236.33/34.80 X344,X340) & 236.33/34.80 X342( 236.33/34.80 X344)))) => 236.33/34.80 (![X346]: 236.33/34.80 ( 236.33/34.80 in( 236.33/34.80 X346,X340) => 236.33/34.80 ( 236.33/34.80 ~ 236.33/34.80 X342( 236.33/34.80 X346)))))) => 236.33/34.80 ((![X348, 236.33/34.80 X350:( 236.33/34.80 ($i > $o))]: 236.33/34.80 ((~ 236.33/34.80 ( 236.33/34.80 ![X352]: 236.33/34.80 (in( 236.33/34.80 X352,X348) => 236.33/34.80 X350( 236.33/34.80 X352)))) => 236.33/34.80 (?[X354]: 236.33/34.80 (in( 236.33/34.80 X354,X348) & 236.33/34.80 (~ 236.33/34.80 X350( 236.33/34.80 X354)))))) => 236.33/34.80 ((![X356:( 236.33/34.80 ($i > $o))]: 236.33/34.80 ((?[X358]: 236.33/34.80 (X356( 236.33/34.80 X358) & 236.33/34.80 (![X360]: 236.33/34.80 (X356( 236.33/34.80 X360) => 236.33/34.80 (X358 = 236.33/34.80 X360))))) => 236.33/34.80 (?[X362]: 236.33/34.80 (X356( 236.33/34.80 X362) & 236.33/34.80 (![X364]: 236.33/34.80 (X356( 236.33/34.80 X364) => 236.33/34.80 (X362 = 236.33/34.80 X364))))))) => 236.33/34.80 ((![X366:( 236.33/34.80 ($i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X368]: 236.33/34.80 X366( 236.33/34.80 X368)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X370, 236.33/34.80 X372]: 236.33/34.80 (X366( 236.33/34.80 X370) => 236.33/34.80 (X366( 236.33/34.80 X372) => 236.33/34.80 (X370 = 236.33/34.80 X372)))) => 236.33/34.80 ( 236.33/34.80 ?[X374]: 236.33/34.80 (X366( 236.33/34.80 X374) & 236.33/34.80 (![X376]: 236.33/34.80 (X366( 236.33/34.80 X376) => 236.33/34.80 (X374 = 236.33/34.80 X376)))))))) => 236.33/34.80 ((![X378:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ?[X380]: 236.33/34.80 (![X382]: 236.33/34.80 (X378( 236.33/34.80 X382) <=> 236.33/34.80 (X382 = 236.33/34.80 X380)))) => 236.33/34.80 ( 236.33/34.80 ?[X384]: 236.33/34.80 (X378( 236.33/34.80 X384) & 236.33/34.80 (![X386]: 236.33/34.80 (X378( 236.33/34.80 X386) => 236.33/34.80 (X384 = 236.33/34.80 X386))))))) => 236.33/34.80 ((![X388, 236.33/34.80 X390]: 236.33/34.80 (( 236.33/34.80 X388 = 236.33/34.80 X390) => 236.33/34.80 (![X392, 236.33/34.80 X394]: 236.33/34.80 (( 236.33/34.80 X392 = 236.33/34.80 X394) => 236.33/34.80 (in( 236.33/34.80 X392,X388) => 236.33/34.80 in( 236.33/34.80 X394,X390)))))) => 236.33/34.80 ((![X396, 236.33/34.80 X398]: 236.33/34.80 (( 236.33/34.80 X396 = 236.33/34.80 X398) => 236.33/34.80 (![X400, 236.33/34.80 X402]: 236.33/34.80 (( 236.33/34.80 X400 = 236.33/34.80 X402) => 236.33/34.80 (in( 236.33/34.80 X400,X396) <=> 236.33/34.80 in( 236.33/34.80 X402,X398)))))) => 236.33/34.80 (( 236.33/34.80 ![X404:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X406]: 236.33/34.80 (X404( 236.33/34.80 X406) & 236.33/34.80 (![X408]: 236.33/34.80 (X404( 236.33/34.80 X408) => 236.33/34.80 (X406 = 236.33/34.80 X408))))) => 236.33/34.80 (![X410, 236.33/34.80 X412]: 236.33/34.80 (X404( 236.33/34.80 X410) => 236.33/34.80 (X404( 236.33/34.80 X412) => 236.33/34.80 (X410 = 236.33/34.80 X412)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X414:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X416:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X418, 236.33/34.80 X420]: 236.33/34.80 (( 236.33/34.80 X418 = 236.33/34.80 X420) => 236.33/34.80 (X414( 236.33/34.80 X418) <=> 236.33/34.80 X416( 236.33/34.80 X420)))) => 236.33/34.80 (( 236.33/34.80 ?[X422]: 236.33/34.80 (X414( 236.33/34.80 X422) & 236.33/34.80 (![X424]: 236.33/34.80 (X414( 236.33/34.80 X424) => 236.33/34.80 (X422 = 236.33/34.80 X424))))) <=> 236.33/34.80 (?[X426]: 236.33/34.80 (X416( 236.33/34.80 X426) & 236.33/34.80 (![X428]: 236.33/34.80 (X416( 236.33/34.80 X428) => 236.33/34.80 (X426 = 236.33/34.80 X428)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 emptyset = 236.33/34.80 emptyset) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X430, 236.33/34.80 X432]: 236.33/34.80 (( 236.33/34.80 X430 = 236.33/34.80 X432) => 236.33/34.80 (![X434, 236.33/34.80 X436]: 236.33/34.80 (( 236.33/34.80 X434 = 236.33/34.80 X436) => 236.33/34.80 (setadjoin( 236.33/34.80 X430,X434) = 236.33/34.80 setadjoin( 236.33/34.80 X432,X436)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X438, 236.33/34.80 X440]: 236.33/34.80 (( 236.33/34.80 X438 = 236.33/34.80 X440) => 236.33/34.80 (powerset( 236.33/34.80 X438) = 236.33/34.80 powerset( 236.33/34.80 X440)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X442, 236.33/34.80 X444]: 236.33/34.80 (( 236.33/34.80 X442 = 236.33/34.80 X444) => 236.33/34.80 (setunion( 236.33/34.80 X442) = 236.33/34.80 setunion( 236.33/34.80 X444)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 omega = 236.33/34.80 omega) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X446:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X448]: 236.33/34.80 (X446( 236.33/34.80 X448) & 236.33/34.80 (![X450]: 236.33/34.80 (X446( 236.33/34.80 X450) => 236.33/34.80 (X448 = 236.33/34.80 X450))))) => 236.33/34.80 (![X452, 236.33/34.80 X454]: 236.33/34.80 (X446( 236.33/34.80 X452) => 236.33/34.80 (X446( 236.33/34.80 X454) => 236.33/34.80 (X452 = 236.33/34.80 X454)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X456:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X458:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X460, 236.33/34.80 X462]: 236.33/34.80 (( 236.33/34.80 X460 = 236.33/34.80 X462) => 236.33/34.80 (X456( 236.33/34.80 X460) <=> 236.33/34.80 X458( 236.33/34.80 X462)))) => 236.33/34.80 (( 236.33/34.80 ?[X464]: 236.33/34.80 (X456( 236.33/34.80 X464) & 236.33/34.80 (![X466]: 236.33/34.80 (X456( 236.33/34.80 X466) => 236.33/34.80 (X464 = 236.33/34.80 X466))))) => 236.33/34.80 (( 236.33/34.80 ?[X468]: 236.33/34.80 (X458( 236.33/34.80 X468) & 236.33/34.80 (![X470]: 236.33/34.80 (X458( 236.33/34.80 X470) => 236.33/34.80 (X468 = 236.33/34.80 X470))))) => 236.33/34.80 (descr( 236.33/34.80 ^[V_9]: 236.33/34.80 X456(V_9)) = 236.33/34.80 descr( 236.33/34.80 ^[V_10]: 236.33/34.80 X458( 236.33/34.80 V_10))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X472, 236.33/34.80 X474]: 236.33/34.80 (( 236.33/34.80 X472 = 236.33/34.80 X474) => 236.33/34.80 (![X476:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X478:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X480]: 236.33/34.80 (in( 236.33/34.80 X480,X472) => 236.33/34.80 (![X482]: 236.33/34.80 (in( 236.33/34.80 X482,X474) => 236.33/34.80 (( 236.33/34.80 X480 = 236.33/34.80 X482) => 236.33/34.80 (X476( 236.33/34.80 X480) <=> 236.33/34.80 X478( 236.33/34.80 X482))))))) => 236.33/34.80 (dsetconstr( 236.33/34.80 X472, 236.33/34.80 ^[V_11]: 236.33/34.80 X476( 236.33/34.80 V_11)) = 236.33/34.80 dsetconstr( 236.33/34.80 X474, 236.33/34.80 ^[V_12]: 236.33/34.80 X478( 236.33/34.80 V_12))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X484, 236.33/34.80 X486]: 236.33/34.80 (( 236.33/34.80 ![X488]: 236.33/34.80 (in( 236.33/34.80 X488,X484) => 236.33/34.80 in( 236.33/34.80 X488,X486))) => 236.33/34.80 subset( 236.33/34.80 X484,X486))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X490, 236.33/34.80 X492]: 236.33/34.80 (( 236.33/34.80 X490 = 236.33/34.80 X492) => 236.33/34.80 subset( 236.33/34.80 X492,X490))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X494, 236.33/34.80 X496]: 236.33/34.80 (( 236.33/34.80 X494 = 236.33/34.80 X496) => 236.33/34.80 subset( 236.33/34.80 X494,X496))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X498, 236.33/34.80 X500]: 236.33/34.80 (( 236.33/34.80 ![X502]: 236.33/34.80 (in( 236.33/34.80 X502,X498) => 236.33/34.80 in( 236.33/34.80 X502,X500))) => 236.33/34.80 subset( 236.33/34.80 X498,X500))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X504]: 236.33/34.80 subset( 236.33/34.80 emptyset, 236.33/34.80 X504)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X506, 236.33/34.80 X508,X510]: 236.33/34.80 (subset( 236.33/34.80 X506,X508) => 236.33/34.80 (in( 236.33/34.80 X510,X506) => 236.33/34.80 in( 236.33/34.80 X510,X508)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X512, 236.33/34.80 X514,X516]: 236.33/34.80 (subset( 236.33/34.80 X512,X514) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X516,X514)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X516,X512))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X518, 236.33/34.80 X520,X522]: 236.33/34.80 (in( 236.33/34.80 X522,X518) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X522,X520)) => 236.33/34.80 (~ 236.33/34.80 subset( 236.33/34.80 X518,X520))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X524, 236.33/34.80 X526]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 subset( 236.33/34.80 X524,X526)) => 236.33/34.80 (X524 != 236.33/34.80 X526))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X528, 236.33/34.80 X530,X532]: 236.33/34.80 (in( 236.33/34.80 X532,X528) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X532,X530)) => 236.33/34.80 (X528 != 236.33/34.80 X530)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X534]: 236.33/34.80 subset( 236.33/34.80 X534,X534)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X536, 236.33/34.80 X538,X540]: 236.33/34.80 (subset( 236.33/34.80 X536,X538) => 236.33/34.80 (subset( 236.33/34.80 X538,X540) => 236.33/34.80 subset( 236.33/34.80 X536,X540)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X542, 236.33/34.80 X544]: 236.33/34.80 subset( 236.33/34.80 X544, 236.33/34.80 setadjoin( 236.33/34.80 X542,X544))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X546, 236.33/34.80 X548,X550]: 236.33/34.80 (subset( 236.33/34.80 X546,X550) => 236.33/34.80 subset( 236.33/34.80 X546, 236.33/34.80 setadjoin( 236.33/34.80 X548,X550)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X552, 236.33/34.80 X554]: 236.33/34.80 (subset( 236.33/34.80 X552,X554) => 236.33/34.80 in( 236.33/34.80 X552, 236.33/34.80 powerset( 236.33/34.80 X554)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X556, 236.33/34.80 X558]: 236.33/34.80 (subset( 236.33/34.80 X556,X558) => 236.33/34.80 (subset( 236.33/34.80 X558,X556) => 236.33/34.80 (X556 = 236.33/34.80 X558)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X560]: 236.33/34.80 (subset( 236.33/34.80 X560, 236.33/34.80 emptyset) => 236.33/34.80 (X560 = 236.33/34.80 emptyset))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X562, 236.33/34.80 X564]: 236.33/34.80 (subset( 236.33/34.80 X564,X562) => 236.33/34.80 in( 236.33/34.80 X564, 236.33/34.80 powerset( 236.33/34.80 X562)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X566, 236.33/34.80 X568]: 236.33/34.80 (in( 236.33/34.80 X568, 236.33/34.80 powerset( 236.33/34.80 X566)) => 236.33/34.80 subset( 236.33/34.80 X568,X566))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X570]: 236.33/34.80 in( 236.33/34.80 X570, 236.33/34.80 powerset( 236.33/34.80 X570))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X572, 236.33/34.80 X574]: 236.33/34.80 (subset( 236.33/34.80 X572,X574) => 236.33/34.80 subset( 236.33/34.80 powerset( 236.33/34.80 X572), 236.33/34.80 powerset( 236.33/34.80 X574)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X576, 236.33/34.80 X578:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 in( 236.33/34.80 dsetconstr( 236.33/34.80 X576, 236.33/34.80 ^[V_13]: 236.33/34.80 X578( 236.33/34.80 V_13)), 236.33/34.80 powerset( 236.33/34.80 X576))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X580, 236.33/34.80 X582:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 subset( 236.33/34.80 dsetconstr( 236.33/34.80 X580, 236.33/34.80 ^[V_14]: 236.33/34.80 X582( 236.33/34.80 V_14)), 236.33/34.80 X580)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X584, 236.33/34.80 X586,X588]: 236.33/34.80 (in( 236.33/34.80 X588,X584) => 236.33/34.80 in( 236.33/34.80 X588, 236.33/34.80 binunion( 236.33/34.80 X584,X586)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X590, 236.33/34.80 X592]: 236.33/34.80 in( 236.33/34.80 X592, 236.33/34.80 setadjoin( 236.33/34.80 X590, 236.33/34.80 setadjoin( 236.33/34.80 X592, 236.33/34.80 emptyset)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X594, 236.33/34.80 X596,X598]: 236.33/34.80 (in( 236.33/34.80 X598,X596) => 236.33/34.80 in( 236.33/34.80 X598, 236.33/34.80 binunion( 236.33/34.80 X594,X596)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X600, 236.33/34.80 X602, 236.33/34.80 X604, 236.33/34.80 X606:$o]: 236.33/34.80 (in( 236.33/34.80 X604, 236.33/34.80 binunion( 236.33/34.80 X600,X602)) => 236.33/34.80 (( 236.33/34.80 in( 236.33/34.80 X604,X600) => 236.33/34.80 X606) => 236.33/34.80 (( 236.33/34.80 in( 236.33/34.80 X604,X602) => 236.33/34.80 X606) => 236.33/34.80 X606)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X608, 236.33/34.80 X610,X612]: 236.33/34.80 (in( 236.33/34.80 X612, 236.33/34.80 binunion( 236.33/34.80 X608,X610)) => 236.33/34.80 (in( 236.33/34.80 X612,X610) | 236.33/34.80 in( 236.33/34.80 X612,X608)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X614, 236.33/34.80 X616]: 236.33/34.80 subset( 236.33/34.80 X614, 236.33/34.80 binunion( 236.33/34.80 X614,X616))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X618, 236.33/34.80 X620]: 236.33/34.80 subset( 236.33/34.80 X620, 236.33/34.80 binunion( 236.33/34.80 X618,X620))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X622, 236.33/34.80 X624,X626]: 236.33/34.80 (in( 236.33/34.80 X626,X622) => 236.33/34.80 (in( 236.33/34.80 X626,X624) => 236.33/34.80 in( 236.33/34.80 X626, 236.33/34.80 binintersect( 236.33/34.80 X622,X624))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X628, 236.33/34.80 X630,X632]: 236.33/34.80 (subset( 236.33/34.80 X632,X628) => 236.33/34.80 (subset( 236.33/34.80 X632,X630) => 236.33/34.80 subset( 236.33/34.80 X632, 236.33/34.80 binintersect( 236.33/34.80 X628,X630))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X634, 236.33/34.80 X636,X638]: 236.33/34.80 (in( 236.33/34.80 X638, 236.33/34.80 binintersect( 236.33/34.80 X634,X636)) => 236.33/34.80 in( 236.33/34.80 X638,X634))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X640, 236.33/34.80 X642]: 236.33/34.80 subset( 236.33/34.80 binintersect( 236.33/34.80 X640,X642), 236.33/34.80 X640)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X644, 236.33/34.80 X646]: 236.33/34.80 (subset( 236.33/34.80 X644,X646) => 236.33/34.80 (binintersect( 236.33/34.80 X644,X646) = 236.33/34.80 X644))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X648, 236.33/34.80 X650]: 236.33/34.80 (( 236.33/34.80 binintersect( 236.33/34.80 X648,X650) = 236.33/34.80 X650) => 236.33/34.80 subset( 236.33/34.80 X650,X648))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X652, 236.33/34.80 X654,X656]: 236.33/34.80 (in( 236.33/34.80 X656, 236.33/34.80 binintersect( 236.33/34.80 X652,X654)) => 236.33/34.80 in( 236.33/34.80 X656,X654))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X658, 236.33/34.80 X660]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 ( 236.33/34.80 ?[X662]: 236.33/34.80 (in( 236.33/34.80 X662,X658) & 236.33/34.80 in( 236.33/34.80 X662,X660)))) => 236.33/34.80 (binintersect( 236.33/34.80 X658,X660) = 236.33/34.80 emptyset))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X664, 236.33/34.80 X666]: 236.33/34.80 subset( 236.33/34.80 binintersect( 236.33/34.80 X664,X666), 236.33/34.80 X666)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X668, 236.33/34.80 X670]: 236.33/34.80 (subset( 236.33/34.80 X670,X668) => 236.33/34.80 (binintersect( 236.33/34.80 X668,X670) = 236.33/34.80 X670))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X672, 236.33/34.80 X674]: 236.33/34.80 (( 236.33/34.80 binintersect( 236.33/34.80 X672,X674) = 236.33/34.80 X672) => 236.33/34.80 subset( 236.33/34.80 X672,X674))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X676, 236.33/34.80 X678,X680]: 236.33/34.80 (binintersect( 236.33/34.80 X676, 236.33/34.80 binunion( 236.33/34.80 X678,X680)) = 236.33/34.80 binunion( 236.33/34.80 binintersect( 236.33/34.80 X676,X678), 236.33/34.80 binintersect( 236.33/34.80 X676,X680)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X682, 236.33/34.80 X684,X686]: 236.33/34.80 (in( 236.33/34.80 X686,X682) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X686,X684)) => 236.33/34.80 in( 236.33/34.80 X686, 236.33/34.80 setminus( 236.33/34.80 X682,X684))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X688, 236.33/34.80 X690,X692]: 236.33/34.80 (in( 236.33/34.80 X692, 236.33/34.80 setminus( 236.33/34.80 X688,X690)) => 236.33/34.80 in( 236.33/34.80 X692,X688))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X694, 236.33/34.80 X696,X698]: 236.33/34.80 (in( 236.33/34.80 X698, 236.33/34.80 setminus( 236.33/34.80 X694,X696)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X698,X696)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X700, 236.33/34.80 X702]: 236.33/34.80 (subset( 236.33/34.80 X700,X702) => 236.33/34.80 (setminus( 236.33/34.80 X700,X702) = 236.33/34.80 emptyset))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X704, 236.33/34.80 X706,X708]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X708, 236.33/34.80 setminus( 236.33/34.80 X704,X706))) => 236.33/34.80 (in( 236.33/34.80 X708,X704) => 236.33/34.80 in( 236.33/34.80 X708,X706)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X710, 236.33/34.80 X712,X714]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X714, 236.33/34.80 setminus( 236.33/34.80 X710,X712))) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X714,X712)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X714,X710))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X716, 236.33/34.80 X718,X720]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X720,X716)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X720, 236.33/34.80 setminus( 236.33/34.80 X716,X718))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X722, 236.33/34.80 X724,X726]: 236.33/34.80 (in( 236.33/34.80 X726,X724) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X726, 236.33/34.80 setminus( 236.33/34.80 X722,X724))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X728, 236.33/34.80 X730]: 236.33/34.80 subset( 236.33/34.80 setminus( 236.33/34.80 X728,X730), 236.33/34.80 X728)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X732, 236.33/34.80 X734]: 236.33/34.80 (( 236.33/34.80 setminus( 236.33/34.80 X732,X734) = 236.33/34.80 emptyset) => 236.33/34.80 subset( 236.33/34.80 X732,X734))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X736, 236.33/34.80 X738,X740]: 236.33/34.80 (in( 236.33/34.80 X740, 236.33/34.80 symdiff( 236.33/34.80 X736,X738)) => 236.33/34.80 (![X742:$o]: 236.33/34.80 (( 236.33/34.80 in( 236.33/34.80 X740,X736) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X740,X738)) => 236.33/34.80 X742)) => 236.33/34.80 (( 236.33/34.80 ( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X740,X736)) => 236.33/34.80 ( 236.33/34.80 in( 236.33/34.80 X740,X738) => 236.33/34.80 X742)) => 236.33/34.80 X742))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X744, 236.33/34.80 X746,X748]: 236.33/34.80 (in( 236.33/34.80 X748,X744) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X748,X746)) => 236.33/34.80 in( 236.33/34.80 X748, 236.33/34.80 symdiff( 236.33/34.80 X744,X746))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X750, 236.33/34.80 X752,X754]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X754,X750)) => 236.33/34.80 (in( 236.33/34.80 X754,X752) => 236.33/34.80 in( 236.33/34.80 X754, 236.33/34.80 symdiff( 236.33/34.80 X750,X752))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X756, 236.33/34.80 X758,X760]: 236.33/34.80 (in( 236.33/34.80 X760,X756) => 236.33/34.80 (in( 236.33/34.80 X760,X758) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X760, 236.33/34.80 symdiff( 236.33/34.80 X756,X758)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X762, 236.33/34.80 X764,X766]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X766,X762)) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X766,X764)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X766, 236.33/34.80 symdiff( 236.33/34.80 X762,X764)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X768, 236.33/34.80 X770]: 236.33/34.80 in( 236.33/34.80 X770, 236.33/34.80 setadjoin( 236.33/34.80 X768, 236.33/34.80 setadjoin( 236.33/34.80 X770, 236.33/34.80 emptyset)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X772, 236.33/34.80 X774]: 236.33/34.80 in( 236.33/34.80 X772, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X772, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X772, 236.33/34.80 setadjoin( 236.33/34.80 X774, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X776, 236.33/34.80 X778]: 236.33/34.80 in( 236.33/34.80 X778, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X776, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X776, 236.33/34.80 setadjoin( 236.33/34.80 X778, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X780, 236.33/34.80 X782]: 236.33/34.80 (?[X784]: 236.33/34.80 (in( 236.33/34.80 X784, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 setadjoin( 236.33/34.80 X782, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (?[X786]: 236.33/34.80 (in( 236.33/34.80 X786, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 setadjoin( 236.33/34.80 X782, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 setadjoin( 236.33/34.80 X782, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)) = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X784, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X784, 236.33/34.80 setadjoin( 236.33/34.80 X786, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X788, 236.33/34.80 X790]: 236.33/34.80 (?[X792]: 236.33/34.80 (in( 236.33/34.80 X792, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 setadjoin( 236.33/34.80 X790, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (?[X794]: 236.33/34.80 (in( 236.33/34.80 X794, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 setadjoin( 236.33/34.80 X790, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 setadjoin( 236.33/34.80 X790, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)) = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X792, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X792, 236.33/34.80 setadjoin( 236.33/34.80 X794, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X796, 236.33/34.80 X798]: 236.33/34.80 (in( 236.33/34.80 X798,X796) => 236.33/34.80 subset( 236.33/34.80 setadjoin( 236.33/34.80 X798, 236.33/34.80 emptyset), 236.33/34.80 X796))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X800, 236.33/34.80 X802]: 236.33/34.80 (in( 236.33/34.80 X802,X800) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 X802, 236.33/34.80 emptyset), 236.33/34.80 powerset( 236.33/34.80 X800)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X804, 236.33/34.80 X806,X808]: 236.33/34.80 (in( 236.33/34.80 X808,X804) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 X808, 236.33/34.80 emptyset), 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X804,X806))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X810, 236.33/34.80 X812,X814]: 236.33/34.80 (in( 236.33/34.80 X814, 236.33/34.80 setadjoin( 236.33/34.80 X810, 236.33/34.80 setadjoin( 236.33/34.80 X812, 236.33/34.80 emptyset))) => 236.33/34.80 (( 236.33/34.80 X814 = 236.33/34.80 X812) | 236.33/34.80 (X814 = 236.33/34.80 X810)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X816, 236.33/34.80 X818,X820]: 236.33/34.80 (in( 236.33/34.80 X820,X816) => 236.33/34.80 (![X822]: 236.33/34.80 (in( 236.33/34.80 X822,X818) => 236.33/34.80 subset( 236.33/34.80 setadjoin( 236.33/34.80 X820, 236.33/34.80 setadjoin( 236.33/34.80 X822, 236.33/34.80 emptyset)), 236.33/34.80 binunion( 236.33/34.80 X816,X818)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X824, 236.33/34.80 X826,X828]: 236.33/34.80 (in( 236.33/34.80 X828,X824) => 236.33/34.80 (![X830]: 236.33/34.80 (in( 236.33/34.80 X830,X826) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 X828, 236.33/34.80 setadjoin( 236.33/34.80 X830, 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X824,X826))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X832, 236.33/34.80 X834,X836]: 236.33/34.80 (in( 236.33/34.80 X836,X832) => 236.33/34.80 (![X838]: 236.33/34.80 (in( 236.33/34.80 X838,X834) => 236.33/34.80 subset( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X836, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X836, 236.33/34.80 setadjoin( 236.33/34.80 X838, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X832,X834))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X840, 236.33/34.80 X842,X844]: 236.33/34.80 (in( 236.33/34.80 X844,X840) => 236.33/34.80 (![X846]: 236.33/34.80 (in( 236.33/34.80 X846,X842) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X844, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X844, 236.33/34.80 setadjoin( 236.33/34.80 X846, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X840,X842)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X848, 236.33/34.80 X850,X852]: 236.33/34.80 (in( 236.33/34.80 X852,X848) => 236.33/34.80 (![X854]: 236.33/34.80 (in( 236.33/34.80 X854,X850) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X852, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X852, 236.33/34.80 setadjoin( 236.33/34.80 X854, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X848,X850)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X856, 236.33/34.80 X858,X860]: 236.33/34.80 (in( 236.33/34.80 X860,X856) => 236.33/34.80 (![X862]: 236.33/34.80 (in( 236.33/34.80 X862,X858) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X860, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X860, 236.33/34.80 setadjoin( 236.33/34.80 X862, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 cartprod( 236.33/34.80 X856,X858)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X864, 236.33/34.80 X866,X868]: 236.33/34.80 (in( 236.33/34.80 X868, 236.33/34.80 cartprod( 236.33/34.80 X864,X866)) => 236.33/34.80 (?[X870]: 236.33/34.80 (in( 236.33/34.80 X870,X864) & 236.33/34.80 (?[X872]: 236.33/34.80 (in( 236.33/34.80 X872,X866) & 236.33/34.80 (X868 = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X870, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X870, 236.33/34.80 setadjoin( 236.33/34.80 X872, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X874, 236.33/34.80 X876,X878]: 236.33/34.80 (in( 236.33/34.80 X878, 236.33/34.80 cartprod( 236.33/34.80 X874,X876)) => 236.33/34.80 (?[X880]: 236.33/34.80 (in( 236.33/34.80 X880, 236.33/34.80 setunion( 236.33/34.80 X878)) & 236.33/34.80 (?[X882]: 236.33/34.80 (in( 236.33/34.80 X882, 236.33/34.80 setunion( 236.33/34.80 X878)) & 236.33/34.80 (X878 = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X880, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X880, 236.33/34.80 setadjoin( 236.33/34.80 X882, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X884, 236.33/34.80 X886]: 236.33/34.80 (in( 236.33/34.80 X886, 236.33/34.80 setunion( 236.33/34.80 X884)) => 236.33/34.80 (?[X888]: 236.33/34.80 (in( 236.33/34.80 X888,X884) & 236.33/34.80 in( 236.33/34.80 X886,X888))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X890]: 236.33/34.80 subset( 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 X890, 236.33/34.80 emptyset)), 236.33/34.80 X890)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X892]: 236.33/34.80 subset( 236.33/34.80 X892, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 X892, 236.33/34.80 emptyset)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X894]: 236.33/34.80 (setunion( 236.33/34.80 setadjoin( 236.33/34.80 X894, 236.33/34.80 emptyset)) = 236.33/34.80 X894)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X896, 236.33/34.80 X898:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X900]: 236.33/34.80 (in( 236.33/34.80 X900,X896) => 236.33/34.80 (![X902]: 236.33/34.80 (in( 236.33/34.80 X902,X896) => 236.33/34.80 (X898( 236.33/34.80 X900) => 236.33/34.80 (X898( 236.33/34.80 X902) => 236.33/34.80 (X900 = 236.33/34.80 X902))))))) => 236.33/34.80 (( 236.33/34.80 ?[X904]: 236.33/34.80 (in( 236.33/34.80 X904,X896) & 236.33/34.80 X898( 236.33/34.80 X904))) => 236.33/34.80 (?[X906]: 236.33/34.80 (in( 236.33/34.80 X906, 236.33/34.80 dsetconstr( 236.33/34.80 X896, 236.33/34.80 ^[V_16]: 236.33/34.80 X898( 236.33/34.80 V_16))) & 236.33/34.80 (dsetconstr( 236.33/34.80 X896, 236.33/34.80 ^[V_15]: 236.33/34.80 X898( 236.33/34.80 V_15)) = 236.33/34.80 setadjoin( 236.33/34.80 X906, 236.33/34.80 emptyset))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X908, 236.33/34.80 X910:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X912]: 236.33/34.80 (in( 236.33/34.80 X912, 236.33/34.80 dsetconstr( 236.33/34.80 X908, 236.33/34.80 ^[V_18]: 236.33/34.80 X910( 236.33/34.80 V_18))) & 236.33/34.80 (dsetconstr( 236.33/34.80 X908, 236.33/34.80 ^[V_17]: 236.33/34.80 X910( 236.33/34.80 V_17)) = 236.33/34.80 setadjoin( 236.33/34.80 X912, 236.33/34.80 emptyset)))) => 236.33/34.80 (?[X914]: 236.33/34.80 (in( 236.33/34.80 X914,X908) & 236.33/34.80 X910( 236.33/34.80 X914))))) => 236.33/34.80 ( 236.33/34.80 ![X916, 236.33/34.80 X918:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X920]: 236.33/34.80 (in( 236.33/34.80 X920,X916) => 236.33/34.80 (X918( 236.33/34.80 X920) => 236.33/34.80 (( 236.33/34.80 ![X922]: 236.33/34.80 (in( 236.33/34.80 X922,X916) => 236.33/34.80 (X918( 236.33/34.80 X922) => 236.33/34.80 (X922 = 236.33/34.80 X920)))) => 236.33/34.80 (?[X924]: 236.33/34.80 (in( 236.33/34.80 X924, 236.33/34.80 dsetconstr( 236.33/34.80 X916, 236.33/34.80 ^[V_20]: 236.33/34.80 X918( 236.33/34.80 V_20))) & 236.33/34.80 (dsetconstr( 236.33/34.80 X916, 236.33/34.80 ^[V_19]: 236.33/34.80 X918( 236.33/34.80 V_19)) = 236.33/34.80 setadjoin( 236.33/34.80 X924, 236.33/34.80 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 236.33/34.80 tff(zf_stmt_1, negated_conjecture, 236.33/34.80 (~ 236.33/34.80 ((![X4,X6]: ((![X8]: (in(X8,X4) <=> in(X8,X6))) => (X4 = X6))) => 236.33/34.80 ((![X10]: (~in(X10,emptyset))) => 236.33/34.80 ((![X12,X14,X16]: 236.33/34.80 (in(X16,setadjoin(X12,X14)) <=> (in(X16,X14) | (X16 = X12)))) => 236.33/34.80 ((![X18,X20]: 236.33/34.80 (in(X20,powerset(X18)) <=> (![X22]: (in(X22,X20) => in(X22,X18))))) => 236.33/34.80 ((![X24,X26]: 236.33/34.80 (in(X26,setunion(X24)) <=> (?[X28]: (in(X26,X28) & in(X28,X24))))) => 236.33/34.80 (in(emptyset,omega) => 236.33/34.80 ((![X30]: (in(X30,omega) => in(setadjoin(X30,X30),omega))) => 236.33/34.80 ((![X32]: 236.33/34.80 (((![X34]: 236.33/34.80 ((in(X34,X32) & in(X34,omega)) => 236.33/34.80 in(setadjoin(X34,X34),X32))) & 236.33/34.80 in(emptyset,X32)) => 236.33/34.80 (![X36]: (in(X36,omega) => in(X36,X32))))) => 236.33/34.80 ((![X38:(($i * $i) > $o),X40]: 236.33/34.80 ((![X42]: 236.33/34.80 (in(X42,X40) => 236.33/34.80 (?[X44]: 236.33/34.80 (X38(X42,X44) & 236.33/34.80 (![X46]: (X38(X42,X46) => (X44 = X46))))))) => 236.33/34.80 (?[X48]: 236.33/34.80 (![X50]: 236.33/34.80 (in(X50,X48) <=> 236.33/34.80 (?[X52]: (in(X52,X40) & X38(X52,X50)))))))) => 236.33/34.80 ((![X54]: 236.33/34.80 ((?[X56]: in(X56,X54)) => 236.33/34.80 (?[X58]: 236.33/34.80 (in(X58,X54) & (~(?[X60]: (in(X60,X58) & in(X60,X54)))))))) => 236.33/34.80 ((![X62]: 236.33/34.80 (?[X64]: 236.33/34.80 ((![X96]: 236.33/34.80 (in(X96,X64) => 236.33/34.80 (![X98]: (in(X98,X96) => in(X98,X62))))) & 236.33/34.80 (![X90,X92]: 236.33/34.80 ((in(X92,X62) & in(X90,X62)) => 236.33/34.80 ((![X94]: 236.33/34.80 (in(X94,X64) => (in(X90,X94) <=> in(X92,X94)))) => 236.33/34.80 (X90 = X92)))) & 236.33/34.80 (![X82,X84]: 236.33/34.80 ((in(X84,X64) & in(X82,X64)) => 236.33/34.80 ((![X88]: (in(X88,X84) => in(X88,X82))) | 236.33/34.80 (![X86]: (in(X86,X82) => in(X86,X84)))))) & 236.33/34.80 (![X66]: 236.33/34.80 (((?[X70]: in(X70,X66)) & 236.33/34.80 (![X68]: (in(X68,X66) => in(X68,X62)))) => 236.33/34.80 (?[X72,X74]: 236.33/34.80 (in(X72,X64) & in(X74,X66) & 236.33/34.80 (~(?[X80]: (in(X80,X72) & in(X80,X66)))) & 236.33/34.80 (![X76]: 236.33/34.80 (in(X76,X64) => 236.33/34.80 (in(X74,X76) | 236.33/34.80 (![X78]: (in(X78,X76) => in(X78,X72))))))))))))) => 236.33/34.80 ((![X100:(($i > $o))]: 236.33/34.80 ((?[X102]: 236.33/34.80 (X100(X102) & (![X104]: (X100(X104) => (X102 = X104))))) => 236.33/34.80 X100(descr(^[V_1]: X100(V_1))))) => 236.33/34.80 ((![X106,X108:(($i > $o)),X110]: 236.33/34.80 (in(X110,X106) => 236.33/34.80 (X108(X110) => 236.33/34.80 in(X110,dsetconstr(X106,^[V_2]: X108(V_2)))))) => 236.33/34.80 ((![X112,X114:(($i > $o)),X116]: 236.33/34.80 (in(X116,dsetconstr(X112,^[V_3]: X114(V_3))) => 236.33/34.80 in(X116,X112))) => 236.33/34.80 ((![X118,X120:(($i > $o)),X122]: 236.33/34.80 (in(X122,dsetconstr(X118,^[V_4]: X120(V_4))) => 236.33/34.80 X120(X122))) => 236.33/34.80 ((![X124:(($i > $o))]: 236.33/34.80 ((?[X126]: 236.33/34.80 (X124(X126) & 236.33/34.80 (![X128]: (X124(X128) => (X126 = X128))))) => 236.33/34.80 (?[X130]: 236.33/34.80 (X124(X130) & 236.33/34.80 (![X132]: (X124(X132) => (X130 = X132))))))) => 236.33/34.80 ((![X134:$o,X136]: (in(X136,prop2set(X134)) => X134)) => 236.33/34.80 ((![X138]: (in(X138,emptyset) => (![X140:$o]: X140))) => 236.33/34.80 ((![X142]: (~in(X142,emptyset))) => 236.33/34.80 ((![X144]: (~in(X144,emptyset))) => 236.33/34.80 ((![X146:(($i > $o))]: 236.33/34.80 ((?[X148]: 236.33/34.80 (X146(X148) & 236.33/34.80 (![X150]: (X146(X150) => (X148 = X150))))) => 236.33/34.80 (?[X152]: X146(X152)))) => 236.33/34.80 ((![X154,X156]: 236.33/34.80 ((![X158]: (in(X158,X154) => in(X158,X156))) => 236.33/34.80 ((![X160]: (in(X160,X156) => in(X160,X154))) => 236.33/34.80 (X154 = X156)))) => 236.33/34.80 ((![X162]: 236.33/34.80 ((![X164]: (~in(X164,X162))) => 236.33/34.80 (X162 = emptyset))) => 236.33/34.80 ((![X166]: 236.33/34.80 ((![X168]: (~in(X168,X166))) => 236.33/34.80 (X166 = emptyset))) => 236.33/34.80 ((![X170,X172:(($i > $o)),X174]: 236.33/34.80 (in(X174,X170) => 236.33/34.80 (in(X174,dsetconstr(X170,^[V_5]: X172(V_5))) <=> 236.33/34.80 X172(X174)))) => 236.33/34.80 ((![X176]: 236.33/34.80 ((X176 != emptyset) => 236.33/34.80 (?[X178]: in(X178,X176)))) => 236.33/34.80 ((![X180,X182:(($i > $o)),X184]: 236.33/34.80 (in(X184,X180) => 236.33/34.80 (X182(X184) => 236.33/34.80 (dsetconstr(X180,^[V_6]: X182(V_6)) != 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X186]: 236.33/34.80 ((?[X188]: in(X188,X186)) => 236.33/34.80 (X186 != emptyset))) => 236.33/34.80 ((![X190,X192]: in(X190,setadjoin(X190,X192))) => 236.33/34.80 (in(emptyset,setadjoin(emptyset,emptyset)) => 236.33/34.80 ((![X194,X196,X198]: 236.33/34.80 (in(X198,X196) => 236.33/34.80 in(X198,setadjoin(X194,X196)))) => 236.33/34.80 ((![X200,X202,X204]: 236.33/34.80 (in(X204,setadjoin(X200,X202)) => 236.33/34.80 (![X206:$o]: 236.33/34.80 (((X204 = X200) => X206) => 236.33/34.80 ((in(X204,X202) => X206) => X206))))) => 236.33/34.80 ((![X208,X210,X212]: 236.33/34.80 (in(X212,setadjoin(X208,X210)) => 236.33/34.80 (in(X212,X210) | (X212 = X208)))) => 236.33/34.80 ((![X214]: 236.33/34.80 (dsetconstr(X214,^[V_7]: $true) = 236.33/34.80 X214)) => 236.33/34.80 ((![X216,X218]: 236.33/34.80 ((![X220]: 236.33/34.80 (in(X220,X218) => in(X220,X216))) => 236.33/34.80 in(X218,powerset(X216)))) => 236.33/34.80 ((![X222]: in(emptyset,powerset(X222))) => 236.33/34.80 ((![X224]: 236.33/34.80 in(emptyset,powerset(X224))) => 236.33/34.80 ((![X226,X228,X230]: 236.33/34.80 (in(X228,powerset(X226)) => 236.33/34.80 (in(X230,X228) => in(X230,X226)))) => 236.33/34.80 ((![X232,X234,X236]: 236.33/34.80 (in(X234,X236) => 236.33/34.80 (in(X236,X232) => 236.33/34.80 in(X234,setunion(X232))))) => 236.33/34.80 ((![X238,X240]: 236.33/34.80 (in(X240,setunion(X238)) => 236.33/34.80 (![X242:$o]: 236.33/34.80 ((![X244]: 236.33/34.80 (in(X240,X244) => 236.33/34.80 (in(X244,X238) => 236.33/34.80 X242))) => 236.33/34.80 X242)))) => 236.33/34.80 ((![X246,X248]: 236.33/34.80 (in(X248,X246) => 236.33/34.80 in(X248, 236.33/34.80 powerset(setunion(X246))))) => 236.33/34.80 ((![X250:(($i > $o))]: 236.33/34.80 ((?[X252]: 236.33/34.80 (X250(X252) & 236.33/34.80 (![X254]: 236.33/34.80 (X250(X254) => 236.33/34.80 (X252 = X254))))) => 236.33/34.80 (?[X256]: 236.33/34.80 (![X258]: 236.33/34.80 (X250(X258) <=> 236.33/34.80 (X258 = X256)))))) => 236.33/34.80 ((![X260]: 236.33/34.80 ((X260 != emptyset) => 236.33/34.80 (?[X262]: in(X262,X260)))) => 236.33/34.80 ((![X264,X266]: 236.33/34.80 (in(X264, 236.33/34.80 setadjoin(X266, 236.33/34.80 emptyset)) => 236.33/34.80 (X264 = X266))) => 236.33/34.80 ((![X268,X270]: 236.33/34.80 ((X268 != X270) => 236.33/34.80 (~ 236.33/34.80 in(X270, 236.33/34.80 setadjoin(X268, 236.33/34.80 emptyset))))) => 236.33/34.80 ((![X272,X274]: 236.33/34.80 ((X272 = X274) => 236.33/34.80 in(X272, 236.33/34.80 setadjoin(X274, 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X276,X278]: 236.33/34.80 (in(X276, 236.33/34.80 setadjoin(X278, 236.33/34.80 emptyset)) => 236.33/34.80 in(X278, 236.33/34.80 setadjoin(X276, 236.33/34.80 emptyset)))) => 236.33/34.80 ((![X280,X282,X284]: 236.33/34.80 (in(X284, 236.33/34.80 setadjoin( 236.33/34.80 X280, 236.33/34.80 setadjoin( 236.33/34.80 X282,emptyset))) => 236.33/34.80 ((X284 = X282) | 236.33/34.80 (X284 = X280)))) => 236.33/34.80 ((![X286,X288]: 236.33/34.80 in(X286, 236.33/34.80 setadjoin( 236.33/34.80 X286, 236.33/34.80 setadjoin( 236.33/34.80 X288,emptyset)))) => 236.33/34.80 ((![X290,X292]: 236.33/34.80 in(X292, 236.33/34.80 setadjoin( 236.33/34.80 X290, 236.33/34.80 setadjoin( 236.33/34.80 X292,emptyset)))) => 236.33/34.80 ((![X294, 236.33/34.80 X296:(($i > $o))]: 236.33/34.80 ((?[X298]: 236.33/34.80 (in(X298,X294) & 236.33/34.80 X296(X298))) => 236.33/34.80 (dsetconstr( 236.33/34.80 X294, 236.33/34.80 ^[V_8]: X296(V_8)) != 236.33/34.80 emptyset))) => 236.33/34.80 ((![X300:(($i > $o)), 236.33/34.80 X302]: 236.33/34.80 (in(X302,emptyset) => 236.33/34.80 X300(X302))) => 236.33/34.80 ((![X304, 236.33/34.80 X306:(($i > $o))]: 236.33/34.80 ((~ 236.33/34.80 (![X308]: 236.33/34.80 (in( 236.33/34.80 X308,X304) => 236.33/34.80 X306(X308)))) => 236.33/34.80 (?[X310]: 236.33/34.80 (in(X310,X304) & 236.33/34.80 (~X306(X310)))))) => 236.33/34.80 ((![X312, 236.33/34.80 X314:(($i > $o))]: 236.33/34.80 ((![X316]: 236.33/34.80 (in( 236.33/34.80 X316,X312) => 236.33/34.80 (~ 236.33/34.80 X314( 236.33/34.80 X316)))) => 236.33/34.80 (~ 236.33/34.80 (?[X318]: 236.33/34.80 (in( 236.33/34.80 X318,X312) & 236.33/34.80 X314( 236.33/34.80 X318)))))) => 236.33/34.80 ((![X320, 236.33/34.80 X322:(($i > $o))]: 236.33/34.80 ((~ 236.33/34.80 (?[X324]: 236.33/34.80 ( 236.33/34.80 in( 236.33/34.80 X324,X320) & 236.33/34.80 X322( 236.33/34.80 X324)))) => 236.33/34.80 (![X326]: 236.33/34.80 (in( 236.33/34.80 X326,X320) => 236.33/34.80 (~ 236.33/34.80 X322( 236.33/34.80 X326)))))) => 236.33/34.80 ((![X328, 236.33/34.80 X330:( 236.33/34.80 ($i > $o))]: 236.33/34.80 ((?[X332]: 236.33/34.80 (in( 236.33/34.80 X332,X328) & 236.33/34.80 ( 236.33/34.80 ~ 236.33/34.80 X330( 236.33/34.80 X332)))) => 236.33/34.80 (~ 236.33/34.80 (![X334]: 236.33/34.80 (in( 236.33/34.80 X334,X328) => 236.33/34.80 X330( 236.33/34.80 X334)))))) => 236.33/34.80 ((![X336:$o]: 236.33/34.80 (X336 => 236.33/34.80 in(emptyset, 236.33/34.80 prop2set( 236.33/34.80 X336)))) => 236.33/34.80 ((![X338:$o]: 236.33/34.80 (X338 => 236.33/34.80 set2prop( 236.33/34.80 prop2set( 236.33/34.80 X338)))) => 236.33/34.80 ((![X340, 236.33/34.80 X342:( 236.33/34.80 ($i > $o))]: 236.33/34.80 ((~ 236.33/34.80 ( 236.33/34.80 ?[X344]: 236.33/34.80 (in( 236.33/34.80 X344,X340) & 236.33/34.80 X342( 236.33/34.80 X344)))) => 236.33/34.80 (![X346]: 236.33/34.80 (in( 236.33/34.80 X346,X340) => 236.33/34.80 (~ 236.33/34.80 X342( 236.33/34.80 X346)))))) => 236.33/34.80 ((![X348, 236.33/34.80 X350:( 236.33/34.80 ($i > $o))]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 ( 236.33/34.80 ![X352]: 236.33/34.80 (in( 236.33/34.80 X352,X348) => 236.33/34.80 X350( 236.33/34.80 X352)))) => 236.33/34.80 ( 236.33/34.80 ?[X354]: 236.33/34.80 (in( 236.33/34.80 X354,X348) & 236.33/34.80 (~ 236.33/34.80 X350( 236.33/34.80 X354)))))) => 236.33/34.80 ((![X356:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ?[X358]: 236.33/34.80 (X356( 236.33/34.80 X358) & 236.33/34.80 (![X360]: 236.33/34.80 (X356( 236.33/34.80 X360) => 236.33/34.80 (X358 = 236.33/34.80 X360))))) => 236.33/34.80 ( 236.33/34.80 ?[X362]: 236.33/34.80 (X356( 236.33/34.80 X362) & 236.33/34.80 (![X364]: 236.33/34.80 (X356( 236.33/34.80 X364) => 236.33/34.80 (X362 = 236.33/34.80 X364))))))) => 236.33/34.80 ((![X366:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X368]: 236.33/34.80 X366( 236.33/34.80 X368)) => 236.33/34.80 (( 236.33/34.80 ![X370, 236.33/34.80 X372]: 236.33/34.80 (X366( 236.33/34.80 X370) => 236.33/34.80 (X366( 236.33/34.80 X372) => 236.33/34.80 (X370 = 236.33/34.80 X372)))) => 236.33/34.80 (?[X374]: 236.33/34.80 (X366( 236.33/34.80 X374) & 236.33/34.80 (![X376]: 236.33/34.80 (X366( 236.33/34.80 X376) => 236.33/34.80 (X374 = 236.33/34.80 X376)))))))) => 236.33/34.80 ((![X378:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X380]: 236.33/34.80 (![X382]: 236.33/34.80 (X378( 236.33/34.80 X382) <=> 236.33/34.80 (X382 = 236.33/34.80 X380)))) => 236.33/34.80 (?[X384]: 236.33/34.80 (X378( 236.33/34.80 X384) & 236.33/34.80 (![X386]: 236.33/34.80 (X378( 236.33/34.80 X386) => 236.33/34.80 (X384 = 236.33/34.80 X386))))))) => 236.33/34.80 (( 236.33/34.80 ![X388, 236.33/34.80 X390]: 236.33/34.80 (( 236.33/34.80 X388 = 236.33/34.80 X390) => 236.33/34.80 (![X392, 236.33/34.80 X394]: 236.33/34.80 (( 236.33/34.80 X392 = 236.33/34.80 X394) => 236.33/34.80 (in( 236.33/34.80 X392,X388) => 236.33/34.80 in( 236.33/34.80 X394,X390)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X396, 236.33/34.80 X398]: 236.33/34.80 (( 236.33/34.80 X396 = 236.33/34.80 X398) => 236.33/34.80 (![X400, 236.33/34.80 X402]: 236.33/34.80 (( 236.33/34.80 X400 = 236.33/34.80 X402) => 236.33/34.80 (in( 236.33/34.80 X400,X396) <=> 236.33/34.80 in( 236.33/34.80 X402,X398)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X404:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X406]: 236.33/34.80 (X404( 236.33/34.80 X406) & 236.33/34.80 (![X408]: 236.33/34.80 (X404( 236.33/34.80 X408) => 236.33/34.80 (X406 = 236.33/34.80 X408))))) => 236.33/34.80 (![X410, 236.33/34.80 X412]: 236.33/34.80 (X404( 236.33/34.80 X410) => 236.33/34.80 (X404( 236.33/34.80 X412) => 236.33/34.80 (X410 = 236.33/34.80 X412)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X414:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X416:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X418, 236.33/34.80 X420]: 236.33/34.80 (( 236.33/34.80 X418 = 236.33/34.80 X420) => 236.33/34.80 (X414( 236.33/34.80 X418) <=> 236.33/34.80 X416( 236.33/34.80 X420)))) => 236.33/34.80 (( 236.33/34.80 ?[X422]: 236.33/34.80 (X414( 236.33/34.80 X422) & 236.33/34.80 (![X424]: 236.33/34.80 (X414( 236.33/34.80 X424) => 236.33/34.80 (X422 = 236.33/34.80 X424))))) <=> 236.33/34.80 (?[X426]: 236.33/34.80 (X416( 236.33/34.80 X426) & 236.33/34.80 (![X428]: 236.33/34.80 (X416( 236.33/34.80 X428) => 236.33/34.80 (X426 = 236.33/34.80 X428)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 emptyset = 236.33/34.80 emptyset) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X430, 236.33/34.80 X432]: 236.33/34.80 (( 236.33/34.80 X430 = 236.33/34.80 X432) => 236.33/34.80 (![X434, 236.33/34.80 X436]: 236.33/34.80 (( 236.33/34.80 X434 = 236.33/34.80 X436) => 236.33/34.80 (setadjoin( 236.33/34.80 X430,X434) = 236.33/34.80 setadjoin( 236.33/34.80 X432,X436)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X438, 236.33/34.80 X440]: 236.33/34.80 (( 236.33/34.80 X438 = 236.33/34.80 X440) => 236.33/34.80 (powerset( 236.33/34.80 X438) = 236.33/34.80 powerset( 236.33/34.80 X440)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X442, 236.33/34.80 X444]: 236.33/34.80 (( 236.33/34.80 X442 = 236.33/34.80 X444) => 236.33/34.80 (setunion( 236.33/34.80 X442) = 236.33/34.80 setunion( 236.33/34.80 X444)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 omega = 236.33/34.80 omega) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X446:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X448]: 236.33/34.80 (X446( 236.33/34.80 X448) & 236.33/34.80 (![X450]: 236.33/34.80 (X446( 236.33/34.80 X450) => 236.33/34.80 (X448 = 236.33/34.80 X450))))) => 236.33/34.80 (![X452, 236.33/34.80 X454]: 236.33/34.80 (X446( 236.33/34.80 X452) => 236.33/34.80 (X446( 236.33/34.80 X454) => 236.33/34.80 (X452 = 236.33/34.80 X454)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X456:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X458:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X460, 236.33/34.80 X462]: 236.33/34.80 (( 236.33/34.80 X460 = 236.33/34.80 X462) => 236.33/34.80 (X456( 236.33/34.80 X460) <=> 236.33/34.80 X458( 236.33/34.80 X462)))) => 236.33/34.80 (( 236.33/34.80 ?[X464]: 236.33/34.80 (X456( 236.33/34.80 X464) & 236.33/34.80 (![X466]: 236.33/34.80 (X456( 236.33/34.80 X466) => 236.33/34.80 (X464 = 236.33/34.80 X466))))) => 236.33/34.80 (( 236.33/34.80 ?[X468]: 236.33/34.80 (X458( 236.33/34.80 X468) & 236.33/34.80 (![X470]: 236.33/34.80 (X458( 236.33/34.80 X470) => 236.33/34.80 (X468 = 236.33/34.80 X470))))) => 236.33/34.80 (descr( 236.33/34.80 ^[V_9]: 236.33/34.80 X456(V_9)) = 236.33/34.80 descr( 236.33/34.80 ^[V_10]: 236.33/34.80 X458( 236.33/34.80 V_10))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X472, 236.33/34.80 X474]: 236.33/34.80 (( 236.33/34.80 X472 = 236.33/34.80 X474) => 236.33/34.80 (![X476:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X478:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X480]: 236.33/34.80 (in( 236.33/34.80 X480,X472) => 236.33/34.80 (![X482]: 236.33/34.80 (in( 236.33/34.80 X482,X474) => 236.33/34.80 (( 236.33/34.80 X480 = 236.33/34.80 X482) => 236.33/34.80 (X476( 236.33/34.80 X480) <=> 236.33/34.80 X478( 236.33/34.80 X482))))))) => 236.33/34.80 (dsetconstr( 236.33/34.80 X472, 236.33/34.80 ^[V_11]: 236.33/34.80 X476( 236.33/34.80 V_11)) = 236.33/34.80 dsetconstr( 236.33/34.80 X474, 236.33/34.80 ^[V_12]: 236.33/34.80 X478( 236.33/34.80 V_12))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X484, 236.33/34.80 X486]: 236.33/34.80 (( 236.33/34.80 ![X488]: 236.33/34.80 (in( 236.33/34.80 X488,X484) => 236.33/34.80 in( 236.33/34.80 X488,X486))) => 236.33/34.80 subset( 236.33/34.80 X484,X486))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X490, 236.33/34.80 X492]: 236.33/34.80 (( 236.33/34.80 X490 = 236.33/34.80 X492) => 236.33/34.80 subset( 236.33/34.80 X492,X490))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X494, 236.33/34.80 X496]: 236.33/34.80 (( 236.33/34.80 X494 = 236.33/34.80 X496) => 236.33/34.80 subset( 236.33/34.80 X494,X496))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X498, 236.33/34.80 X500]: 236.33/34.80 (( 236.33/34.80 ![X502]: 236.33/34.80 (in( 236.33/34.80 X502,X498) => 236.33/34.80 in( 236.33/34.80 X502,X500))) => 236.33/34.80 subset( 236.33/34.80 X498,X500))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X504]: 236.33/34.80 subset( 236.33/34.80 emptyset, 236.33/34.80 X504)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X506, 236.33/34.80 X508,X510]: 236.33/34.80 (subset( 236.33/34.80 X506,X508) => 236.33/34.80 (in( 236.33/34.80 X510,X506) => 236.33/34.80 in( 236.33/34.80 X510,X508)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X512, 236.33/34.80 X514,X516]: 236.33/34.80 (subset( 236.33/34.80 X512,X514) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X516,X514)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X516,X512))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X518, 236.33/34.80 X520,X522]: 236.33/34.80 (in( 236.33/34.80 X522,X518) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X522,X520)) => 236.33/34.80 (~ 236.33/34.80 subset( 236.33/34.80 X518,X520))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X524, 236.33/34.80 X526]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 subset( 236.33/34.80 X524,X526)) => 236.33/34.80 (X524 != 236.33/34.80 X526))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X528, 236.33/34.80 X530,X532]: 236.33/34.80 (in( 236.33/34.80 X532,X528) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X532,X530)) => 236.33/34.80 (X528 != 236.33/34.80 X530)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X534]: 236.33/34.80 subset( 236.33/34.80 X534,X534)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X536, 236.33/34.80 X538,X540]: 236.33/34.80 (subset( 236.33/34.80 X536,X538) => 236.33/34.80 (subset( 236.33/34.80 X538,X540) => 236.33/34.80 subset( 236.33/34.80 X536,X540)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X542, 236.33/34.80 X544]: 236.33/34.80 subset( 236.33/34.80 X544, 236.33/34.80 setadjoin( 236.33/34.80 X542,X544))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X546, 236.33/34.80 X548,X550]: 236.33/34.80 (subset( 236.33/34.80 X546,X550) => 236.33/34.80 subset( 236.33/34.80 X546, 236.33/34.80 setadjoin( 236.33/34.80 X548,X550)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X552, 236.33/34.80 X554]: 236.33/34.80 (subset( 236.33/34.80 X552,X554) => 236.33/34.80 in( 236.33/34.80 X552, 236.33/34.80 powerset( 236.33/34.80 X554)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X556, 236.33/34.80 X558]: 236.33/34.80 (subset( 236.33/34.80 X556,X558) => 236.33/34.80 (subset( 236.33/34.80 X558,X556) => 236.33/34.80 (X556 = 236.33/34.80 X558)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X560]: 236.33/34.80 (subset( 236.33/34.80 X560, 236.33/34.80 emptyset) => 236.33/34.80 (X560 = 236.33/34.80 emptyset))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X562, 236.33/34.80 X564]: 236.33/34.80 (subset( 236.33/34.80 X564,X562) => 236.33/34.80 in( 236.33/34.80 X564, 236.33/34.80 powerset( 236.33/34.80 X562)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X566, 236.33/34.80 X568]: 236.33/34.80 (in( 236.33/34.80 X568, 236.33/34.80 powerset( 236.33/34.80 X566)) => 236.33/34.80 subset( 236.33/34.80 X568,X566))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X570]: 236.33/34.80 in( 236.33/34.80 X570, 236.33/34.80 powerset( 236.33/34.80 X570))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X572, 236.33/34.80 X574]: 236.33/34.80 (subset( 236.33/34.80 X572,X574) => 236.33/34.80 subset( 236.33/34.80 powerset( 236.33/34.80 X572), 236.33/34.80 powerset( 236.33/34.80 X574)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X576, 236.33/34.80 X578:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 in( 236.33/34.80 dsetconstr( 236.33/34.80 X576, 236.33/34.80 ^[V_13]: 236.33/34.80 X578( 236.33/34.80 V_13)), 236.33/34.80 powerset( 236.33/34.80 X576))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X580, 236.33/34.80 X582:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 subset( 236.33/34.80 dsetconstr( 236.33/34.80 X580, 236.33/34.80 ^[V_14]: 236.33/34.80 X582( 236.33/34.80 V_14)), 236.33/34.80 X580)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X584, 236.33/34.80 X586,X588]: 236.33/34.80 (in( 236.33/34.80 X588,X584) => 236.33/34.80 in( 236.33/34.80 X588, 236.33/34.80 binunion( 236.33/34.80 X584,X586)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X590, 236.33/34.80 X592]: 236.33/34.80 in( 236.33/34.80 X592, 236.33/34.80 setadjoin( 236.33/34.80 X590, 236.33/34.80 setadjoin( 236.33/34.80 X592, 236.33/34.80 emptyset)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X594, 236.33/34.80 X596,X598]: 236.33/34.80 (in( 236.33/34.80 X598,X596) => 236.33/34.80 in( 236.33/34.80 X598, 236.33/34.80 binunion( 236.33/34.80 X594,X596)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X600, 236.33/34.80 X602, 236.33/34.80 X604, 236.33/34.80 X606:$o]: 236.33/34.80 (in( 236.33/34.80 X604, 236.33/34.80 binunion( 236.33/34.80 X600,X602)) => 236.33/34.80 (( 236.33/34.80 in( 236.33/34.80 X604,X600) => 236.33/34.80 X606) => 236.33/34.80 (( 236.33/34.80 in( 236.33/34.80 X604,X602) => 236.33/34.80 X606) => 236.33/34.80 X606)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X608, 236.33/34.80 X610,X612]: 236.33/34.80 (in( 236.33/34.80 X612, 236.33/34.80 binunion( 236.33/34.80 X608,X610)) => 236.33/34.80 (in( 236.33/34.80 X612,X610) | 236.33/34.80 in( 236.33/34.80 X612,X608)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X614, 236.33/34.80 X616]: 236.33/34.80 subset( 236.33/34.80 X614, 236.33/34.80 binunion( 236.33/34.80 X614,X616))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X618, 236.33/34.80 X620]: 236.33/34.80 subset( 236.33/34.80 X620, 236.33/34.80 binunion( 236.33/34.80 X618,X620))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X622, 236.33/34.80 X624,X626]: 236.33/34.80 (in( 236.33/34.80 X626,X622) => 236.33/34.80 (in( 236.33/34.80 X626,X624) => 236.33/34.80 in( 236.33/34.80 X626, 236.33/34.80 binintersect( 236.33/34.80 X622,X624))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X628, 236.33/34.80 X630,X632]: 236.33/34.80 (subset( 236.33/34.80 X632,X628) => 236.33/34.80 (subset( 236.33/34.80 X632,X630) => 236.33/34.80 subset( 236.33/34.80 X632, 236.33/34.80 binintersect( 236.33/34.80 X628,X630))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X634, 236.33/34.80 X636,X638]: 236.33/34.80 (in( 236.33/34.80 X638, 236.33/34.80 binintersect( 236.33/34.80 X634,X636)) => 236.33/34.80 in( 236.33/34.80 X638,X634))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X640, 236.33/34.80 X642]: 236.33/34.80 subset( 236.33/34.80 binintersect( 236.33/34.80 X640,X642), 236.33/34.80 X640)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X644, 236.33/34.80 X646]: 236.33/34.80 (subset( 236.33/34.80 X644,X646) => 236.33/34.80 (binintersect( 236.33/34.80 X644,X646) = 236.33/34.80 X644))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X648, 236.33/34.80 X650]: 236.33/34.80 (( 236.33/34.80 binintersect( 236.33/34.80 X648,X650) = 236.33/34.80 X650) => 236.33/34.80 subset( 236.33/34.80 X650,X648))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X652, 236.33/34.80 X654,X656]: 236.33/34.80 (in( 236.33/34.80 X656, 236.33/34.80 binintersect( 236.33/34.80 X652,X654)) => 236.33/34.80 in( 236.33/34.80 X656,X654))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X658, 236.33/34.80 X660]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 ( 236.33/34.80 ?[X662]: 236.33/34.80 (in( 236.33/34.80 X662,X658) & 236.33/34.80 in( 236.33/34.80 X662,X660)))) => 236.33/34.80 (binintersect( 236.33/34.80 X658,X660) = 236.33/34.80 emptyset))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X664, 236.33/34.80 X666]: 236.33/34.80 subset( 236.33/34.80 binintersect( 236.33/34.80 X664,X666), 236.33/34.80 X666)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X668, 236.33/34.80 X670]: 236.33/34.80 (subset( 236.33/34.80 X670,X668) => 236.33/34.80 (binintersect( 236.33/34.80 X668,X670) = 236.33/34.80 X670))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X672, 236.33/34.80 X674]: 236.33/34.80 (( 236.33/34.80 binintersect( 236.33/34.80 X672,X674) = 236.33/34.80 X672) => 236.33/34.80 subset( 236.33/34.80 X672,X674))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X676, 236.33/34.80 X678,X680]: 236.33/34.80 (binintersect( 236.33/34.80 X676, 236.33/34.80 binunion( 236.33/34.80 X678,X680)) = 236.33/34.80 binunion( 236.33/34.80 binintersect( 236.33/34.80 X676,X678), 236.33/34.80 binintersect( 236.33/34.80 X676,X680)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X682, 236.33/34.80 X684,X686]: 236.33/34.80 (in( 236.33/34.80 X686,X682) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X686,X684)) => 236.33/34.80 in( 236.33/34.80 X686, 236.33/34.80 setminus( 236.33/34.80 X682,X684))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X688, 236.33/34.80 X690,X692]: 236.33/34.80 (in( 236.33/34.80 X692, 236.33/34.80 setminus( 236.33/34.80 X688,X690)) => 236.33/34.80 in( 236.33/34.80 X692,X688))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X694, 236.33/34.80 X696,X698]: 236.33/34.80 (in( 236.33/34.80 X698, 236.33/34.80 setminus( 236.33/34.80 X694,X696)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X698,X696)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X700, 236.33/34.80 X702]: 236.33/34.80 (subset( 236.33/34.80 X700,X702) => 236.33/34.80 (setminus( 236.33/34.80 X700,X702) = 236.33/34.80 emptyset))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X704, 236.33/34.80 X706,X708]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X708, 236.33/34.80 setminus( 236.33/34.80 X704,X706))) => 236.33/34.80 (in( 236.33/34.80 X708,X704) => 236.33/34.80 in( 236.33/34.80 X708,X706)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X710, 236.33/34.80 X712,X714]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X714, 236.33/34.80 setminus( 236.33/34.80 X710,X712))) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X714,X712)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X714,X710))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X716, 236.33/34.80 X718,X720]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X720,X716)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X720, 236.33/34.80 setminus( 236.33/34.80 X716,X718))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X722, 236.33/34.80 X724,X726]: 236.33/34.80 (in( 236.33/34.80 X726,X724) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X726, 236.33/34.80 setminus( 236.33/34.80 X722,X724))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X728, 236.33/34.80 X730]: 236.33/34.80 subset( 236.33/34.80 setminus( 236.33/34.80 X728,X730), 236.33/34.80 X728)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X732, 236.33/34.80 X734]: 236.33/34.80 (( 236.33/34.80 setminus( 236.33/34.80 X732,X734) = 236.33/34.80 emptyset) => 236.33/34.80 subset( 236.33/34.80 X732,X734))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X736, 236.33/34.80 X738,X740]: 236.33/34.80 (in( 236.33/34.80 X740, 236.33/34.80 symdiff( 236.33/34.80 X736,X738)) => 236.33/34.80 (![X742:$o]: 236.33/34.80 (( 236.33/34.80 in( 236.33/34.80 X740,X736) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X740,X738)) => 236.33/34.80 X742)) => 236.33/34.80 (( 236.33/34.80 ( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X740,X736)) => 236.33/34.80 ( 236.33/34.80 in( 236.33/34.80 X740,X738) => 236.33/34.80 X742)) => 236.33/34.80 X742))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X744, 236.33/34.80 X746,X748]: 236.33/34.80 (in( 236.33/34.80 X748,X744) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X748,X746)) => 236.33/34.80 in( 236.33/34.80 X748, 236.33/34.80 symdiff( 236.33/34.80 X744,X746))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X750, 236.33/34.80 X752,X754]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X754,X750)) => 236.33/34.80 (in( 236.33/34.80 X754,X752) => 236.33/34.80 in( 236.33/34.80 X754, 236.33/34.80 symdiff( 236.33/34.80 X750,X752))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X756, 236.33/34.80 X758,X760]: 236.33/34.80 (in( 236.33/34.80 X760,X756) => 236.33/34.80 (in( 236.33/34.80 X760,X758) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X760, 236.33/34.80 symdiff( 236.33/34.80 X756,X758)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X762, 236.33/34.80 X764,X766]: 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X766,X762)) => 236.33/34.80 (( 236.33/34.80 ~ 236.33/34.80 in( 236.33/34.80 X766,X764)) => 236.33/34.80 (~ 236.33/34.80 in( 236.33/34.80 X766, 236.33/34.80 symdiff( 236.33/34.80 X762,X764)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X768, 236.33/34.80 X770]: 236.33/34.80 in( 236.33/34.80 X770, 236.33/34.80 setadjoin( 236.33/34.80 X768, 236.33/34.80 setadjoin( 236.33/34.80 X770, 236.33/34.80 emptyset)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X772, 236.33/34.80 X774]: 236.33/34.80 in( 236.33/34.80 X772, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X772, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X772, 236.33/34.80 setadjoin( 236.33/34.80 X774, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X776, 236.33/34.80 X778]: 236.33/34.80 in( 236.33/34.80 X778, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X776, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X776, 236.33/34.80 setadjoin( 236.33/34.80 X778, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X780, 236.33/34.80 X782]: 236.33/34.80 (?[X784]: 236.33/34.80 (in( 236.33/34.80 X784, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 setadjoin( 236.33/34.80 X782, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (?[X786]: 236.33/34.80 (in( 236.33/34.80 X786, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 setadjoin( 236.33/34.80 X782, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X780, 236.33/34.80 setadjoin( 236.33/34.80 X782, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)) = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X784, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X784, 236.33/34.80 setadjoin( 236.33/34.80 X786, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X788, 236.33/34.80 X790]: 236.33/34.80 (?[X792]: 236.33/34.80 (in( 236.33/34.80 X792, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 setadjoin( 236.33/34.80 X790, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (?[X794]: 236.33/34.80 (in( 236.33/34.80 X794, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 setadjoin( 236.33/34.80 X790, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))) & 236.33/34.80 (setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X788, 236.33/34.80 setadjoin( 236.33/34.80 X790, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)) = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X792, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X792, 236.33/34.80 setadjoin( 236.33/34.80 X794, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X796, 236.33/34.80 X798]: 236.33/34.80 (in( 236.33/34.80 X798,X796) => 236.33/34.80 subset( 236.33/34.80 setadjoin( 236.33/34.80 X798, 236.33/34.80 emptyset), 236.33/34.80 X796))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X800, 236.33/34.80 X802]: 236.33/34.80 (in( 236.33/34.80 X802,X800) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 X802, 236.33/34.80 emptyset), 236.33/34.80 powerset( 236.33/34.80 X800)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X804, 236.33/34.80 X806,X808]: 236.33/34.80 (in( 236.33/34.80 X808,X804) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 X808, 236.33/34.80 emptyset), 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X804,X806))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X810, 236.33/34.80 X812,X814]: 236.33/34.80 (in( 236.33/34.80 X814, 236.33/34.80 setadjoin( 236.33/34.80 X810, 236.33/34.80 setadjoin( 236.33/34.80 X812, 236.33/34.80 emptyset))) => 236.33/34.80 (( 236.33/34.80 X814 = 236.33/34.80 X812) | 236.33/34.80 (X814 = 236.33/34.80 X810)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X816, 236.33/34.80 X818,X820]: 236.33/34.80 (in( 236.33/34.80 X820,X816) => 236.33/34.80 (![X822]: 236.33/34.80 (in( 236.33/34.80 X822,X818) => 236.33/34.80 subset( 236.33/34.80 setadjoin( 236.33/34.80 X820, 236.33/34.80 setadjoin( 236.33/34.80 X822, 236.33/34.80 emptyset)), 236.33/34.80 binunion( 236.33/34.80 X816,X818)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X824, 236.33/34.80 X826,X828]: 236.33/34.80 (in( 236.33/34.80 X828,X824) => 236.33/34.80 (![X830]: 236.33/34.80 (in( 236.33/34.80 X830,X826) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 X828, 236.33/34.80 setadjoin( 236.33/34.80 X830, 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X824,X826))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X832, 236.33/34.80 X834,X836]: 236.33/34.80 (in( 236.33/34.80 X836,X832) => 236.33/34.80 (![X838]: 236.33/34.80 (in( 236.33/34.80 X838,X834) => 236.33/34.80 subset( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X836, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X836, 236.33/34.80 setadjoin( 236.33/34.80 X838, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X832,X834))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X840, 236.33/34.80 X842,X844]: 236.33/34.80 (in( 236.33/34.80 X844,X840) => 236.33/34.80 (![X846]: 236.33/34.80 (in( 236.33/34.80 X846,X842) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X844, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X844, 236.33/34.80 setadjoin( 236.33/34.80 X846, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X840,X842)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X848, 236.33/34.80 X850,X852]: 236.33/34.80 (in( 236.33/34.80 X852,X848) => 236.33/34.80 (![X854]: 236.33/34.80 (in( 236.33/34.80 X854,X850) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X852, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X852, 236.33/34.80 setadjoin( 236.33/34.80 X854, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 powerset( 236.33/34.80 powerset( 236.33/34.80 binunion( 236.33/34.80 X848,X850)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X856, 236.33/34.80 X858,X860]: 236.33/34.80 (in( 236.33/34.80 X860,X856) => 236.33/34.80 (![X862]: 236.33/34.80 (in( 236.33/34.80 X862,X858) => 236.33/34.80 in( 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X860, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X860, 236.33/34.80 setadjoin( 236.33/34.80 X862, 236.33/34.80 emptyset)), 236.33/34.80 emptyset)), 236.33/34.80 cartprod( 236.33/34.80 X856,X858)))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X864, 236.33/34.80 X866,X868]: 236.33/34.80 (in( 236.33/34.80 X868, 236.33/34.80 cartprod( 236.33/34.80 X864,X866)) => 236.33/34.80 (?[X870]: 236.33/34.80 (in( 236.33/34.80 X870,X864) & 236.33/34.80 (?[X872]: 236.33/34.80 (in( 236.33/34.80 X872,X866) & 236.33/34.80 (X868 = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X870, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X870, 236.33/34.80 setadjoin( 236.33/34.80 X872, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X874, 236.33/34.80 X876,X878]: 236.33/34.80 (in( 236.33/34.80 X878, 236.33/34.80 cartprod( 236.33/34.80 X874,X876)) => 236.33/34.80 (?[X880]: 236.33/34.80 (in( 236.33/34.80 X880, 236.33/34.80 setunion( 236.33/34.80 X878)) & 236.33/34.80 (?[X882]: 236.33/34.80 (in( 236.33/34.80 X882, 236.33/34.80 setunion( 236.33/34.80 X878)) & 236.33/34.80 (X878 = 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X880, 236.33/34.80 emptyset), 236.33/34.80 setadjoin( 236.33/34.80 setadjoin( 236.33/34.80 X880, 236.33/34.80 setadjoin( 236.33/34.80 X882, 236.33/34.80 emptyset)), 236.33/34.80 emptyset))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X884, 236.33/34.80 X886]: 236.33/34.80 (in( 236.33/34.80 X886, 236.33/34.80 setunion( 236.33/34.80 X884)) => 236.33/34.80 (?[X888]: 236.33/34.80 (in( 236.33/34.80 X888,X884) & 236.33/34.80 in( 236.33/34.80 X886,X888))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X890]: 236.33/34.80 subset( 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 X890, 236.33/34.80 emptyset)), 236.33/34.80 X890)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X892]: 236.33/34.80 subset( 236.33/34.80 X892, 236.33/34.80 setunion( 236.33/34.80 setadjoin( 236.33/34.80 X892, 236.33/34.80 emptyset)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X894]: 236.33/34.80 (setunion( 236.33/34.80 setadjoin( 236.33/34.80 X894, 236.33/34.80 emptyset)) = 236.33/34.80 X894)) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X896, 236.33/34.80 X898:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ![X900]: 236.33/34.80 (in( 236.33/34.80 X900,X896) => 236.33/34.80 (![X902]: 236.33/34.80 (in( 236.33/34.80 X902,X896) => 236.33/34.80 (X898( 236.33/34.80 X900) => 236.33/34.80 (X898( 236.33/34.80 X902) => 236.33/34.80 (X900 = 236.33/34.80 X902))))))) => 236.33/34.80 (( 236.33/34.80 ?[X904]: 236.33/34.80 (in( 236.33/34.80 X904,X896) & 236.33/34.80 X898( 236.33/34.80 X904))) => 236.33/34.80 (?[X906]: 236.33/34.80 (in( 236.33/34.80 X906, 236.33/34.80 dsetconstr( 236.33/34.80 X896, 236.33/34.80 ^[V_16]: 236.33/34.80 X898( 236.33/34.80 V_16))) & 236.33/34.80 (dsetconstr( 236.33/34.80 X896, 236.33/34.80 ^[V_15]: 236.33/34.80 X898( 236.33/34.80 V_15)) = 236.33/34.80 setadjoin( 236.33/34.80 X906, 236.33/34.80 emptyset))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 ![X908, 236.33/34.80 X910:( 236.33/34.80 ( 236.33/34.80 $i > $o))]: 236.33/34.80 (( 236.33/34.80 ?[X912]: 236.33/34.80 (in( 236.33/34.80 X912, 236.33/34.80 dsetconstr( 236.33/34.80 X908, 236.33/34.80 ^[V_18]: 236.33/34.80 X910( 236.33/34.80 V_18))) & 236.33/34.80 (dsetconstr( 236.33/34.80 X908, 236.33/34.80 ^[V_17]: 236.33/34.80 X910( 236.33/34.80 V_17)) = 236.33/34.80 setadjoin( 236.33/34.80 X912, 236.33/34.80 emptyset)))) => 236.33/34.80 (?[X914]: 236.33/34.80 (in( 236.33/34.80 X914,X908) & 236.33/34.80 X910( 236.33/34.80 X914))))) => 236.33/34.80 ( 236.33/34.80 ![X916, 236.33/34.80 X918:( 236.33/34.80 ( 236.33/34.80 $i > $o)), 236.33/34.80 X920]: 236.33/34.80 (in( 236.33/34.80 X920,X916) => 236.33/34.80 (X918( 236.33/34.80 X920) => 236.33/34.80 (( 236.33/34.80 ![X922]: 236.33/34.80 (in( 236.33/34.80 X922,X916) => 236.33/34.80 (X918( 236.33/34.80 X922) => 236.33/34.80 (X922 = 236.33/34.80 X920)))) => 236.33/34.80 (?[X924]: 236.33/34.80 (in( 236.33/34.80 X924, 236.33/34.80 dsetconstr( 236.33/34.80 X916, 236.33/34.80 ^[V_20]: 236.33/34.80 X918( 236.33/34.80 V_20))) & 236.33/34.80 (dsetconstr( 236.33/34.80 X916, 236.33/34.80 ^[V_19]: 236.33/34.80 X918( 236.33/34.80 V_19)) = 236.33/34.80 setadjoin( 236.33/34.80 X924, 236.33/34.80 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))). 236.33/34.80 tff('169', plain, 236.33/34.80 ~ ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 ((!!((^[Y2 : $i]: (in(Y2, Y0) <=> in(Y2, Y1))))) => 236.33/34.80 (Y0 = Y1)))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, setadjoin(Y0, Y1)) <=> 236.33/34.80 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (in(Y1, powerset(Y0)) <=> 236.33/34.80 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (in(Y1, setunion(Y0)) <=> 236.33/34.80 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 236.33/34.80 (in(emptyset, omega) => 236.33/34.80 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (((!!((^[Y1 : $i]: 236.33/34.80 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.80 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.80 in(emptyset, Y0)) => 236.33/34.80 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.80 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 ((!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y1) => 236.33/34.80 (??((^[Y3 : $i]: 236.33/34.80 (Y0(Y2, Y3) & 236.33/34.80 (!!((^[Y4 : $i]: 236.33/34.80 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.80 (??((^[Y2 : $i]: 236.33/34.80 (!!((^[Y3 : $i]: 236.33/34.80 (in(Y3, Y2) <=> 236.33/34.80 (??((^[Y4 : $i]: 236.33/34.80 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.80 (??((^[Y1 : $i]: 236.33/34.80 (in(Y1, Y0) & 236.33/34.80 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (??((^[Y1 : $i]: 236.33/34.80 ((!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y1) => 236.33/34.80 (!!((^[Y3 : $i]: 236.33/34.80 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (!!((^[Y3 : $i]: 236.33/34.80 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.80 ((!!((^[Y4 : $i]: 236.33/34.80 (in(Y4, Y1) => 236.33/34.80 (in(Y2, Y4) <=> 236.33/34.80 in(Y3, Y4)))))) => 236.33/34.80 (Y2 = Y3)))))))))& 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (!!((^[Y3 : $i]: 236.33/34.80 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.80 ((!!((^[Y4 : $i]: 236.33/34.80 (in(Y4, Y3) => 236.33/34.80 in(Y4, Y2))))) | 236.33/34.80 (!!((^[Y4 : $i]: 236.33/34.80 (in(Y4, Y2) => 236.33/34.80 in(Y4, Y3)))))))))))))& 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.80 (!!((^[Y3 : $i]: 236.33/34.80 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.80 (??((^[Y3 : $i]: 236.33/34.80 (??((^[Y4 : $i]: 236.33/34.80 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.80 (~((??((^[Y5 : $i]: 236.33/34.80 (in(Y5, Y3) & 236.33/34.80 in(Y5, Y2)))))))& 236.33/34.80 (!!((^[Y5 : $i]: 236.33/34.80 (in(Y5, Y1) => 236.33/34.80 (in(Y4, Y5) | 236.33/34.80 (!!(( 236.33/34.80 ^[Y6 : $i]: 236.33/34.80 (in(Y6, 236.33/34.80 Y5) => 236.33/34.80 in(Y6, 236.33/34.80 Y3)))))))))))))))))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i > $o]: 236.33/34.80 ((??((^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.80 Y0(descr((^[Y1 : $i]: Y0(Y1)))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i > $o]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y0) => 236.33/34.80 (Y1(Y2) => 236.33/34.80 in(Y2, 236.33/34.80 dsetconstr(Y0, 236.33/34.80 (^[Y3 : $i]: Y1(Y3))))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i > $o]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 dsetconstr(Y0, 236.33/34.80 (^[Y3 : $i]: Y1(Y3)))) => 236.33/34.80 in(Y2, Y0))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i > $o]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 dsetconstr(Y0, 236.33/34.80 (^[Y3 : $i]: Y1(Y3)))) => 236.33/34.80 Y1(Y2))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i > $o]: 236.33/34.80 ((??((^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.80 (??((^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $o]: 236.33/34.80 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.80 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.80 ((!!((^[Y0 : $i > $o]: 236.33/34.80 ((??((^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.80 (??((^[Y1 : $i]: Y0(Y1)))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 ((!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.80 ((!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.80 (Y0 = Y1))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.80 (Y0 = emptyset))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.80 (Y0 = emptyset))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i > $o]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y0) => 236.33/34.80 (in(Y2, 236.33/34.80 dsetconstr(Y0, 236.33/34.80 (^[Y3 : $i]: Y1(Y3)))) <=> 236.33/34.80 Y1(Y2)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 ((Y0 != emptyset) => 236.33/34.80 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i > $o]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y0) => 236.33/34.80 (Y1(Y2) => 236.33/34.80 (dsetconstr(Y0, 236.33/34.80 (^[Y3 : $i]: 236.33/34.80 Y1(Y3))) != 236.33/34.80 emptyset)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.80 (Y0 != emptyset))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.80 (in(emptyset, 236.33/34.80 setadjoin(emptyset, emptyset)) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y1) => 236.33/34.80 in(Y2, 236.33/34.80 setadjoin(Y0, 236.33/34.80 Y1)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 setadjoin(Y0, 236.33/34.80 Y1)) => 236.33/34.80 (!!((^[Y3 : $o]: 236.33/34.80 (( 236.33/34.80 ( 236.33/34.80 Y2 = Y0) => 236.33/34.80 Y3) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 in(Y2, 236.33/34.80 Y1) => Y3) => 236.33/34.80 Y3))))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 setadjoin(Y0, 236.33/34.80 Y1)) => 236.33/34.80 (in(Y2, Y1) | 236.33/34.80 (Y2 = Y0)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (dsetconstr(Y0, 236.33/34.80 (^[Y1 : $i]: $true)) = 236.33/34.80 Y0)))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 ((!!((^[Y2 : $i]: 236.33/34.80 (in(Y2, Y1) => 236.33/34.80 in(Y2, Y0))))) => 236.33/34.80 in(Y1, powerset(Y0))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 in(emptyset, powerset(Y0))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 in(emptyset, powerset(Y0))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y1, 236.33/34.80 powerset( 236.33/34.80 Y0)) => 236.33/34.80 (in(Y2, Y1) => 236.33/34.80 in(Y2, Y0)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (in(Y1, Y2) => 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 in(Y1, 236.33/34.80 setunion( 236.33/34.80 Y0))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (in(Y1, 236.33/34.80 setunion(Y0)) => 236.33/34.80 (!!((^[Y2 : $o]: 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (in(Y1, 236.33/34.80 Y3) => 236.33/34.80 (in(Y3, 236.33/34.80 Y0) => Y2))))) => 236.33/34.80 Y2))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (in(Y1, Y0) => 236.33/34.80 in(Y1, 236.33/34.80 powerset( 236.33/34.80 setunion( 236.33/34.80 Y0)))))))))) => 236.33/34.80 ((!!((^[Y0 : $i > $o]: 236.33/34.80 ((??((^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => 236.33/34.80 ( 236.33/34.80 Y1 = Y2))))))))) => 236.33/34.80 (??((^[Y1 : $i]: 236.33/34.80 (!!((^[Y2 : $i]: 236.33/34.80 (Y0(Y2) <=> 236.33/34.80 (Y2 = Y1)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 ((Y0 != emptyset) => 236.33/34.80 (??((^[Y1 : $i]: 236.33/34.80 in(Y1, Y0)))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (in(Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, 236.33/34.80 emptyset)) => 236.33/34.80 (Y0 = Y1)))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 ((Y0 != Y1) => 236.33/34.80 (~( 236.33/34.80 in(Y1, 236.33/34.80 setadjoin( 236.33/34.80 Y0, 236.33/34.80 emptyset))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 ((Y0 = Y1) => 236.33/34.80 in(Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, 236.33/34.80 emptyset))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 (in(Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, 236.33/34.80 emptyset)) => 236.33/34.80 in(Y1, 236.33/34.80 setadjoin( 236.33/34.80 Y0, 236.33/34.80 emptyset))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 setadjoin( 236.33/34.80 Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, 236.33/34.80 emptyset))) => 236.33/34.80 (( 236.33/34.80 Y2 = Y1) | 236.33/34.80 (Y2 = Y0)))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 in(Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, 236.33/34.80 emptyset))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!((^[Y1 : $i]: 236.33/34.80 in(Y1, 236.33/34.80 setadjoin( 236.33/34.80 Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, 236.33/34.80 emptyset))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) & 236.33/34.80 Y1(Y2))))) => 236.33/34.80 ( 236.33/34.80 dsetconstr( 236.33/34.80 Y0, 236.33/34.80 (^[Y2 : $i]: 236.33/34.80 Y1(Y2))) != 236.33/34.80 emptyset)))))))) => 236.33/34.80 ((!!((^[Y0 : $i > $o]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 ( 236.33/34.80 in(Y1, 236.33/34.80 emptyset) => 236.33/34.80 Y0(Y1)))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ~(( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 Y1(Y2))))))) => 236.33/34.80 (??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) & 236.33/34.80 (~( 236.33/34.80 Y1(Y2)))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 (~( 236.33/34.80 Y1(Y2))))))) => 236.33/34.80 (~(( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) & 236.33/34.80 Y1(Y2)))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ~(( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) & 236.33/34.80 Y1(Y2))))))) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 (~( 236.33/34.80 Y1(Y2)))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) & 236.33/34.80 (~( 236.33/34.80 Y1(Y2))))))) => 236.33/34.80 (~(( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 Y1(Y2)))))))))))))) => 236.33/34.80 ((!!((^[Y0 : $o]: 236.33/34.80 (Y0 => 236.33/34.80 in( 236.33/34.80 emptyset, 236.33/34.80 prop2set( 236.33/34.80 Y0)))))) => 236.33/34.80 ((!!(( 236.33/34.80 ^[Y0 : $o]: 236.33/34.80 (Y0 => 236.33/34.80 set2prop( 236.33/34.80 prop2set( 236.33/34.80 Y0)))))) => 236.33/34.80 ((!!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ~(( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) & 236.33/34.80 Y1(Y2))))))) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 (~( 236.33/34.80 Y1(Y2)))))))))))))) => 236.33/34.80 ((!!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ~(( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 Y1(Y2))))))) => 236.33/34.80 (??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) & 236.33/34.80 (~( 236.33/34.80 Y1(Y2)))))))))))))) => 236.33/34.80 ((!!(( 236.33/34.80 ^[Y0 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))) => 236.33/34.80 (??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))))))) => 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 Y0(Y1)))) => 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y1) => 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))) => 236.33/34.80 (??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2)))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) <=> 236.33/34.80 (Y2 = Y1)))))))) => 236.33/34.80 (??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (( 236.33/34.80 Y2 = Y3) => 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 in(Y3, 236.33/34.80 Y1)))))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (( 236.33/34.80 Y2 = Y3) => 236.33/34.80 (in(Y2, 236.33/34.80 Y0) <=> 236.33/34.80 in(Y3, 236.33/34.80 Y1)))))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y1) => 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i > $o]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (( 236.33/34.80 Y2 = Y3) => 236.33/34.80 (Y0(Y2) <=> 236.33/34.80 Y1(Y3))))))))) => 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (Y0(Y3) => 236.33/34.80 (Y2 = Y3))))))))) <=> 236.33/34.80 (??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y1(Y2) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (Y1(Y3) => 236.33/34.80 (Y2 = Y3))))))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 emptyset = 236.33/34.80 emptyset) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (( 236.33/34.80 Y2 = Y3) => 236.33/34.80 (setadjoin( 236.33/34.80 Y0, Y2) = 236.33/34.80 setadjoin( 236.33/34.80 Y1, Y3)))))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 (powerset( 236.33/34.80 Y0) = 236.33/34.80 powerset( 236.33/34.80 Y1))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 (setunion( 236.33/34.80 Y0) = 236.33/34.80 setunion( 236.33/34.80 Y1))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 omega = 236.33/34.80 omega) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i > $o]: 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (Y0(Y1) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y1) => 236.33/34.80 (Y0(Y2) => 236.33/34.80 (Y1 = Y2))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i > $o]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (( 236.33/34.80 Y2 = Y3) => 236.33/34.80 (Y0(Y2) <=> 236.33/34.80 Y1(Y3))))))))) => 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y0(Y2) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (Y0(Y3) => 236.33/34.80 (Y2 = Y3))))))))) => 236.33/34.80 (( 236.33/34.80 ??(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (Y1(Y2) & 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i]: 236.33/34.80 (Y1(Y3) => 236.33/34.80 (Y2 = Y3))))))))) => 236.33/34.80 (descr( 236.33/34.80 (^[Y2 : $i]: 236.33/34.80 Y0(Y2))) = 236.33/34.80 descr( 236.33/34.80 (^[Y2 : $i]: 236.33/34.80 Y1(Y2))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i > $o]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y3 : $i > $o]: 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y4 : $i]: 236.33/34.80 (in(Y4, 236.33/34.80 Y0) => 236.33/34.80 (!!(( 236.33/34.80 ^[Y5 : $i]: 236.33/34.80 (in(Y5, 236.33/34.80 Y1) => 236.33/34.80 (( 236.33/34.80 Y4 = Y5) => 236.33/34.80 (Y2(Y4) <=> 236.33/34.80 Y3(Y5))))))))))) => 236.33/34.80 (dsetconstr( 236.33/34.80 Y0, 236.33/34.80 (^[Y4 : $i]: 236.33/34.80 Y2(Y4))) = 236.33/34.80 dsetconstr( 236.33/34.80 Y1, 236.33/34.80 (^[Y4 : $i]: 236.33/34.80 Y3(Y4)))))))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 in(Y2, 236.33/34.80 Y1))))) => 236.33/34.80 subset( 236.33/34.80 Y0, Y1)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 subset( 236.33/34.80 Y1, Y0)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 Y0 = Y1) => 236.33/34.80 subset( 236.33/34.80 Y0, Y1)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 !!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 in(Y2, 236.33/34.80 Y1))))) => 236.33/34.80 subset( 236.33/34.80 Y0, Y1)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 subset( 236.33/34.80 emptyset, 236.33/34.80 Y0)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, Y1) => 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 in(Y2, 236.33/34.80 Y1)))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, Y1) => 236.33/34.80 (( 236.33/34.80 ~( 236.33/34.80 in(Y2, 236.33/34.80 Y1))) => 236.33/34.80 (~( 236.33/34.80 in(Y2, 236.33/34.80 Y0)))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 (( 236.33/34.80 ~( 236.33/34.80 in(Y2, 236.33/34.80 Y1))) => 236.33/34.80 (~( 236.33/34.80 subset( 236.33/34.80 Y0, Y1)))))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (( 236.33/34.80 ~( 236.33/34.80 subset( 236.33/34.80 Y0, Y1))) => 236.33/34.80 (Y0 != Y1)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 (( 236.33/34.80 ~( 236.33/34.80 in(Y2, 236.33/34.80 Y1))) => 236.33/34.80 (Y0 != Y1)))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 subset( 236.33/34.80 Y0, Y0)))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, Y1) => 236.33/34.80 (subset( 236.33/34.80 Y1, Y2) => 236.33/34.80 subset( 236.33/34.80 Y0, Y2)))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 subset( 236.33/34.80 Y1, 236.33/34.80 setadjoin( 236.33/34.80 Y0, Y1)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, Y2) => 236.33/34.80 subset( 236.33/34.80 Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, Y2)))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, Y1) => 236.33/34.80 in(Y0, 236.33/34.80 powerset( 236.33/34.80 Y1))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, Y1) => 236.33/34.80 (subset( 236.33/34.80 Y1, Y0) => 236.33/34.80 (Y0 = Y1))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, 236.33/34.80 emptyset) => 236.33/34.80 (Y0 = 236.33/34.80 emptyset))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y1, Y0) => 236.33/34.80 in(Y1, 236.33/34.80 powerset( 236.33/34.80 Y0))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (in(Y1, 236.33/34.80 powerset( 236.33/34.80 Y0)) => 236.33/34.80 subset( 236.33/34.80 Y1, Y0)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 in(Y0, 236.33/34.80 powerset( 236.33/34.80 Y0))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (subset( 236.33/34.80 Y0, Y1) => 236.33/34.80 subset( 236.33/34.80 powerset( 236.33/34.80 Y0), 236.33/34.80 powerset( 236.33/34.80 Y1))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 in( 236.33/34.80 dsetconstr( 236.33/34.80 Y0, 236.33/34.80 (^[Y2 : $i]: 236.33/34.80 Y1(Y2))), 236.33/34.80 powerset( 236.33/34.80 Y0)))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i > $o]: 236.33/34.80 subset( 236.33/34.80 dsetconstr( 236.33/34.80 Y0, 236.33/34.80 (^[Y2 : $i]: 236.33/34.80 Y1(Y2))), 236.33/34.80 Y0))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y0) => 236.33/34.80 in(Y2, 236.33/34.80 binunion( 236.33/34.80 Y0, Y1)))))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 in(Y1, 236.33/34.80 setadjoin( 236.33/34.80 Y0, 236.33/34.80 setadjoin( 236.33/34.80 Y1, 236.33/34.80 emptyset))))))))) => 236.33/34.80 ( 236.33/34.80 ( 236.33/34.80 !!(( 236.33/34.80 ^[Y0 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y1 : $i]: 236.33/34.80 (!!(( 236.33/34.80 ^[Y2 : $i]: 236.33/34.80 (in(Y2, 236.33/34.80 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $o]: 236.33/34.81 (in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y0) => Y3) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) | 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y1, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y2, Y0) => 236.33/34.81 (subset( 236.33/34.81 Y2, Y1) => 236.33/34.81 subset( 236.33/34.81 Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y0))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 Y1, Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 Y1))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y1, Y0) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y0) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (binintersect( 236.33/34.81 Y0, 236.33/34.81 binunion( 236.33/34.81 Y1, Y2)) = 236.33/34.81 binunion( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 binintersect( 236.33/34.81 Y0, Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y0))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (setminus( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 setminus( 236.33/34.81 Y0, Y1), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 setminus( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $o]: 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y0) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 Y3)) => 236.33/34.81 (( 236.33/34.81 ( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 ( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3)) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y0, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)) = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)) = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y0) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset), 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y0) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset), 236.33/34.81 powerset( 236.33/34.81 Y0))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))) => 236.33/34.81 (( 236.33/34.81 Y2 = Y1) | 236.33/34.81 (Y2 = Y0)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) & 236.33/34.81 (??(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 Y1) & 236.33/34.81 (Y2 = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 setadjoin( 236.33/34.81 Y4, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 Y2)) & 236.33/34.81 (??(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 setunion( 236.33/34.81 Y2)) & 236.33/34.81 (Y2 = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 setadjoin( 236.33/34.81 Y4, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 setunion( 236.33/34.81 Y0)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 in(Y1, 236.33/34.81 Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)), 236.33/34.81 Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)) = 236.33/34.81 Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y2 = Y3))))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3)))) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3))) = 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3)))) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3))) = 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset)))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y3 = Y2)))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y4 : $i]: 236.33/34.81 Y1(Y4)))) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y4 : $i]: 236.33/34.81 Y1(Y4))) = 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.81 inference('cnf', [status(esa)], [zf_stmt_1])). 236.33/34.81 tff('170', plain, 236.33/34.81 ~ ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: (in(Y2, Y0) <=> in(Y2, Y1))))) => 236.33/34.81 (Y0 = Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, setadjoin(Y0, Y1)) <=> 236.33/34.81 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, powerset(Y0)) <=> 236.33/34.81 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, setunion(Y0)) <=> 236.33/34.81 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 236.33/34.81 (in(emptyset, omega) => 236.33/34.81 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (((!!((^[Y1 : $i]: 236.33/34.81 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.81 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.81 in(emptyset, Y0)) => 236.33/34.81 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.81 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 (??((^[Y3 : $i]: 236.33/34.81 (Y0(Y2, Y3) & 236.33/34.81 (!!((^[Y4 : $i]: 236.33/34.81 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.81 (??((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) <=> 236.33/34.81 (??((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 (in(Y1, Y0) & 236.33/34.81 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.81 ((!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y1) => 236.33/34.81 (in(Y2, Y4) <=> 236.33/34.81 in(Y3, Y4)))))) => 236.33/34.81 (Y2 = Y3)))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.81 ((!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y3) => 236.33/34.81 in(Y4, Y2))))) | 236.33/34.81 (!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y2) => 236.33/34.81 in(Y4, Y3)))))))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.81 (??((^[Y3 : $i]: 236.33/34.81 (??((^[Y4 : $i]: 236.33/34.81 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.81 (~((??((^[Y5 : $i]: 236.33/34.81 (in(Y5, Y3) & 236.33/34.81 in(Y5, Y2)))))))& 236.33/34.81 (!!((^[Y5 : $i]: 236.33/34.81 (in(Y5, Y1) => 236.33/34.81 (in(Y4, Y5) | 236.33/34.81 (!!(( 236.33/34.81 ^[Y6 : $i]: 236.33/34.81 (in(Y6, 236.33/34.81 Y5) => 236.33/34.81 in(Y6, 236.33/34.81 Y3)))))))))))))))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 ((??((^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.81 Y0(descr((^[Y1 : $i]: Y0(Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 in(Y2, 236.33/34.81 dsetconstr(Y0, 236.33/34.81 (^[Y3 : $i]: Y1(Y3))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr(Y0, 236.33/34.81 (^[Y3 : $i]: Y1(Y3)))) => 236.33/34.81 in(Y2, Y0))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr(Y0, 236.33/34.81 (^[Y3 : $i]: Y1(Y3)))) => 236.33/34.81 Y1(Y2))))))))))) => 236.33/34.81 ((!!((^[Y0 : $o]: 236.33/34.81 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 ((??((^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.81 (??((^[Y1 : $i]: Y0(Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.81 (Y0 = Y1))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.81 (Y0 = emptyset))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.81 (Y0 = emptyset))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr(Y0, 236.33/34.81 (^[Y3 : $i]: Y1(Y3)))) <=> 236.33/34.81 Y1(Y2)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((Y0 != emptyset) => 236.33/34.81 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (dsetconstr(Y0, 236.33/34.81 (^[Y3 : $i]: Y1(Y3))) != 236.33/34.81 emptyset)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.81 (Y0 != emptyset))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.81 (in(emptyset, 236.33/34.81 setadjoin(emptyset, emptyset)) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 in(Y2, 236.33/34.81 setadjoin(Y0, Y1)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin(Y0, 236.33/34.81 Y1)) => 236.33/34.81 (!!((^[Y3 : $o]: 236.33/34.81 ((( 236.33/34.81 Y2 = Y0) => 236.33/34.81 Y3) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin(Y0, 236.33/34.81 Y1)) => 236.33/34.81 (in(Y2, Y1) | 236.33/34.81 (Y2 = Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (dsetconstr(Y0, 236.33/34.81 (^[Y1 : $i]: $true)) = 236.33/34.81 Y0)))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 in(Y2, Y0))))) => 236.33/34.81 in(Y1, powerset(Y0))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 in(emptyset, powerset(Y0))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 in(emptyset, powerset(Y0))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 powerset( 236.33/34.81 Y0)) => 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 in(Y2, Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y1, Y2) => 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 in(Y1, 236.33/34.81 setunion( 236.33/34.81 Y0))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 setunion(Y0)) => 236.33/34.81 (!!((^[Y2 : $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y3) => 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => Y2))))) => 236.33/34.81 Y2))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, Y0) => 236.33/34.81 in(Y1, 236.33/34.81 powerset( 236.33/34.81 setunion(Y0)))))))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 ((??((^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 (Y2 = Y1)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((Y0 != emptyset) => 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 in(Y1, Y0)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)) => 236.33/34.81 (Y0 = Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((Y0 != Y1) => 236.33/34.81 (~(in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((Y0 = Y1) => 236.33/34.81 in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)) => 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))) => 236.33/34.81 (( 236.33/34.81 Y2 = Y1) | 236.33/34.81 (Y2 = Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))) => 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y2 : $i]: 236.33/34.81 Y1(Y2))) != 236.33/34.81 emptyset)))))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 emptyset) => 236.33/34.81 Y0(Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 ~(( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 ( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (~( 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 (~( 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (~(( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $o]: 236.33/34.81 (Y0 => 236.33/34.81 in( 236.33/34.81 emptyset, 236.33/34.81 prop2set( 236.33/34.81 Y0)))))) => 236.33/34.81 ((!!((^[Y0 : $o]: 236.33/34.81 (Y0 => 236.33/34.81 set2prop( 236.33/34.81 prop2set( 236.33/34.81 Y0)))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 Y0(Y1)))) => 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y1) => 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2)))))))))))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 (Y2 = Y1)))))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))))))) => 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y3, 236.33/34.81 Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) <=> 236.33/34.81 in(Y3, 236.33/34.81 Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y1) => 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 Y1(Y3))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y0(Y3) => 236.33/34.81 (Y2 = Y3))))))))) <=> 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y1(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y2 = Y3))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (setadjoin( 236.33/34.81 Y0, Y2) = 236.33/34.81 setadjoin( 236.33/34.81 Y1, Y3)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (powerset( 236.33/34.81 Y0) = 236.33/34.81 powerset( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (setunion( 236.33/34.81 Y0) = 236.33/34.81 setunion( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y1) => 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 Y1(Y3))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y0(Y3) => 236.33/34.81 (Y2 = Y3))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y1(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y2 = Y3))))))))) => 236.33/34.81 (descr( 236.33/34.81 (^[Y2 : $i]: 236.33/34.81 Y0(Y2))) = 236.33/34.81 descr( 236.33/34.81 (^[Y2 : $i]: 236.33/34.81 Y1(Y2))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y5 : $i]: 236.33/34.81 (in(Y5, 236.33/34.81 Y1) => 236.33/34.81 (( 236.33/34.81 Y4 = Y5) => 236.33/34.81 (Y2(Y4) <=> 236.33/34.81 Y3(Y5))))))))))) => 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y4 : $i]: 236.33/34.81 Y2(Y4))) = 236.33/34.81 dsetconstr( 236.33/34.81 Y1, 236.33/34.81 (^[Y4 : $i]: 236.33/34.81 Y3(Y4)))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1))))) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 subset( 236.33/34.81 Y1, Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1))))) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 emptyset, 236.33/34.81 Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 subset( 236.33/34.81 Y0, Y1))) => 236.33/34.81 (Y0 != Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (Y0 != Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (subset( 236.33/34.81 Y1, Y2) => 236.33/34.81 subset( 236.33/34.81 Y0, Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y2) => 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 in(Y0, 236.33/34.81 powerset( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (subset( 236.33/34.81 Y1, Y0) => 236.33/34.81 (Y0 = Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, 236.33/34.81 emptyset) => 236.33/34.81 (Y0 = 236.33/34.81 emptyset))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y1, Y0) => 236.33/34.81 in(Y1, 236.33/34.81 powerset( 236.33/34.81 Y0))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 powerset( 236.33/34.81 Y0)) => 236.33/34.81 subset( 236.33/34.81 Y1, Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 in(Y0, 236.33/34.81 powerset( 236.33/34.81 Y0))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 subset( 236.33/34.81 powerset( 236.33/34.81 Y0), 236.33/34.81 powerset( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 in( 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y2 : $i]: 236.33/34.81 Y1(Y2))), 236.33/34.81 powerset( 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 subset( 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y2 : $i]: 236.33/34.81 Y1(Y2))), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $o]: 236.33/34.81 (in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y0) => Y3) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) | 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y1, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y2, Y0) => 236.33/34.81 (subset( 236.33/34.81 Y2, Y1) => 236.33/34.81 subset( 236.33/34.81 Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y0))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 Y1, Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 Y1))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y1, Y0) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y0) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (binintersect( 236.33/34.81 Y0, 236.33/34.81 binunion( 236.33/34.81 Y1, Y2)) = 236.33/34.81 binunion( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 binintersect( 236.33/34.81 Y0, Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y0))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (setminus( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 setminus( 236.33/34.81 Y0, Y1), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 setminus( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $o]: 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y0) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 Y3)) => 236.33/34.81 (( 236.33/34.81 ( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 ( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3)) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y0, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)) = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)) = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y0) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset), 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y0) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset), 236.33/34.81 powerset( 236.33/34.81 Y0))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))) => 236.33/34.81 (( 236.33/34.81 Y2 = Y1) | 236.33/34.81 (Y2 = Y0)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) & 236.33/34.81 (??(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 Y1) & 236.33/34.81 (Y2 = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 setadjoin( 236.33/34.81 Y4, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 Y2)) & 236.33/34.81 (??(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 setunion( 236.33/34.81 Y2)) & 236.33/34.81 (Y2 = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 setadjoin( 236.33/34.81 Y4, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 setunion( 236.33/34.81 Y0)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 in(Y1, 236.33/34.81 Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)), 236.33/34.81 Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)) = 236.33/34.81 Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y2 = Y3))))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3)))) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3))) = 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3)))) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y3 : $i]: 236.33/34.81 Y1(Y3))) = 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset)))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y3 = Y2)))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y4 : $i]: 236.33/34.81 Y1(Y4)))) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, 236.33/34.81 (^[Y4 : $i]: 236.33/34.81 Y1(Y4))) = 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.81 inference('simplify boolean subterms', [status(thm)], ['169'])). 236.33/34.81 tff('171', plain, 236.33/34.81 ~ ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: (in(Y2, Y0) <=> in(Y2, Y1))))) => 236.33/34.81 (Y0 = Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, setadjoin(Y0, Y1)) <=> 236.33/34.81 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, powerset(Y0)) <=> 236.33/34.81 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, setunion(Y0)) <=> 236.33/34.81 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 236.33/34.81 (in(emptyset, omega) => 236.33/34.81 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (((!!((^[Y1 : $i]: 236.33/34.81 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.81 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.81 in(emptyset, Y0)) => 236.33/34.81 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.81 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 (??((^[Y3 : $i]: 236.33/34.81 (Y0(Y2, Y3) & 236.33/34.81 (!!((^[Y4 : $i]: 236.33/34.81 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.81 (??((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) <=> 236.33/34.81 (??((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 (in(Y1, Y0) & 236.33/34.81 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.81 ((!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y1) => 236.33/34.81 (in(Y2, Y4) <=> 236.33/34.81 in(Y3, Y4)))))) => 236.33/34.81 (Y2 = Y3)))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.81 ((!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y3) => 236.33/34.81 in(Y4, Y2))))) | 236.33/34.81 (!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y2) => 236.33/34.81 in(Y4, Y3)))))))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.81 (??((^[Y3 : $i]: 236.33/34.81 (??((^[Y4 : $i]: 236.33/34.81 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.81 (~((??((^[Y5 : $i]: 236.33/34.81 (in(Y5, Y3) & 236.33/34.81 in(Y5, Y2)))))))& 236.33/34.81 (!!((^[Y5 : $i]: 236.33/34.81 (in(Y5, Y1) => 236.33/34.81 (in(Y4, Y5) | 236.33/34.81 (!!(( 236.33/34.81 ^[Y6 : $i]: 236.33/34.81 (in(Y6, 236.33/34.81 Y5) => 236.33/34.81 in(Y6, 236.33/34.81 Y3)))))))))))))))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 ((??((^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.81 Y0(descr(Y0)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, dsetconstr(Y0, Y1)) => 236.33/34.81 in(Y2, Y0))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, dsetconstr(Y0, Y1)) => 236.33/34.81 Y1(Y2))))))))))) => 236.33/34.81 ((!!((^[Y0 : $o]: 236.33/34.81 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 ((??((^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.81 (??(Y0)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.81 (Y0 = Y1))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.81 (Y0 = emptyset))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.81 (Y0 = emptyset))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr(Y0, Y1)) <=> 236.33/34.81 Y1(Y2)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((Y0 != emptyset) => 236.33/34.81 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (dsetconstr(Y0, Y1) != 236.33/34.81 emptyset)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.81 (Y0 != emptyset))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.81 (in(emptyset, 236.33/34.81 setadjoin(emptyset, emptyset)) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 in(Y2, 236.33/34.81 setadjoin(Y0, Y1)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin(Y0, 236.33/34.81 Y1)) => 236.33/34.81 (!!((^[Y3 : $o]: 236.33/34.81 ((( 236.33/34.81 Y2 = Y0) => 236.33/34.81 Y3) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin(Y0, 236.33/34.81 Y1)) => 236.33/34.81 (in(Y2, Y1) | 236.33/34.81 (Y2 = Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (dsetconstr(Y0, 236.33/34.81 (^[Y1 : $i]: $true)) = 236.33/34.81 Y0)))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 in(Y2, Y0))))) => 236.33/34.81 in(Y1, powerset(Y0))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 in(emptyset, powerset(Y0))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 in(emptyset, powerset(Y0))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 powerset( 236.33/34.81 Y0)) => 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 in(Y2, Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y1, Y2) => 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 in(Y1, 236.33/34.81 setunion( 236.33/34.81 Y0))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 setunion(Y0)) => 236.33/34.81 (!!((^[Y2 : $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y3) => 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => Y2))))) => 236.33/34.81 Y2))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, Y0) => 236.33/34.81 in(Y1, 236.33/34.81 powerset( 236.33/34.81 setunion(Y0)))))))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 ((??((^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 (Y2 = Y1)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((Y0 != emptyset) => 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 in(Y1, Y0)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)) => 236.33/34.81 (Y0 = Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((Y0 != Y1) => 236.33/34.81 (~(in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((Y0 = Y1) => 236.33/34.81 in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)) => 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))) => 236.33/34.81 (( 236.33/34.81 Y2 = Y1) | 236.33/34.81 (Y2 = Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 in(Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))) => 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, Y1) != 236.33/34.81 emptyset)))))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 emptyset) => 236.33/34.81 Y0(Y1)))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 ~(( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 ( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (~( 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 (~( 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (~(( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $o]: 236.33/34.81 (Y0 => 236.33/34.81 in( 236.33/34.81 emptyset, 236.33/34.81 prop2set( 236.33/34.81 Y0)))))) => 236.33/34.81 ((!!((^[Y0 : $o]: 236.33/34.81 (Y0 => 236.33/34.81 set2prop( 236.33/34.81 prop2set( 236.33/34.81 Y0)))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 Y1(Y2))))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 (~( 236.33/34.81 Y1(Y2)))))))))))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(Y0)) => 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y1) => 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2)))))))))))))) => 236.33/34.81 ((!!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 (Y2 = Y1)))))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))))))) => 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y3, 236.33/34.81 Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) <=> 236.33/34.81 in(Y3, 236.33/34.81 Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y1) => 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 Y1(Y3))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y0(Y3) => 236.33/34.81 (Y2 = Y3))))))))) <=> 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y1(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y2 = Y3))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (setadjoin( 236.33/34.81 Y0, Y2) = 236.33/34.81 setadjoin( 236.33/34.81 Y1, Y3)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (powerset( 236.33/34.81 Y0) = 236.33/34.81 powerset( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (setunion( 236.33/34.81 Y0) = 236.33/34.81 setunion( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y1) => 236.33/34.81 (Y0(Y2) => 236.33/34.81 (Y1 = Y2))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (( 236.33/34.81 Y2 = Y3) => 236.33/34.81 (Y0(Y2) <=> 236.33/34.81 Y1(Y3))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y0(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y0(Y3) => 236.33/34.81 (Y2 = Y3))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (Y1(Y2) & 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y2 = Y3))))))))) => 236.33/34.81 (descr( 236.33/34.81 Y0) = 236.33/34.81 descr(Y1))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y5 : $i]: 236.33/34.81 (in(Y5, 236.33/34.81 Y1) => 236.33/34.81 (( 236.33/34.81 Y4 = Y5) => 236.33/34.81 (Y2(Y4) <=> 236.33/34.81 Y3(Y5))))))))))) => 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, Y2) = 236.33/34.81 dsetconstr( 236.33/34.81 Y1, Y3)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1))))) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 subset( 236.33/34.81 Y1, Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 Y0 = Y1) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1))))) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!( 236.33/34.81 subset( 236.33/34.81 emptyset))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 subset( 236.33/34.81 Y0, Y1))) => 236.33/34.81 (Y0 != Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (Y0 != Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (subset( 236.33/34.81 Y1, Y2) => 236.33/34.81 subset( 236.33/34.81 Y0, Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y2) => 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 in(Y0, 236.33/34.81 powerset( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (subset( 236.33/34.81 Y1, Y0) => 236.33/34.81 (Y0 = Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, 236.33/34.81 emptyset) => 236.33/34.81 (Y0 = 236.33/34.81 emptyset))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y1, Y0) => 236.33/34.81 in(Y1, 236.33/34.81 powerset( 236.33/34.81 Y0))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 powerset( 236.33/34.81 Y0)) => 236.33/34.81 subset( 236.33/34.81 Y1, Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 in(Y0, 236.33/34.81 powerset( 236.33/34.81 Y0))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 subset( 236.33/34.81 powerset( 236.33/34.81 Y0), 236.33/34.81 powerset( 236.33/34.81 Y1))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 in( 236.33/34.81 dsetconstr( 236.33/34.81 Y0, Y1), 236.33/34.81 powerset( 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 subset( 236.33/34.81 dsetconstr( 236.33/34.81 Y0, Y1), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $o]: 236.33/34.81 (in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y0) => Y3) => 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) | 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 Y1, 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y2, Y0) => 236.33/34.81 (subset( 236.33/34.81 Y2, Y1) => 236.33/34.81 subset( 236.33/34.81 Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y0))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 Y1, Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 ~(( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 Y1))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y1, Y0) => 236.33/34.81 (binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1) = 236.33/34.81 Y0) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (binintersect( 236.33/34.81 Y0, 236.33/34.81 binunion( 236.33/34.81 Y1, Y2)) = 236.33/34.81 binunion( 236.33/34.81 binintersect( 236.33/34.81 Y0, Y1), 236.33/34.81 binintersect( 236.33/34.81 Y0, Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)) => 236.33/34.81 in(Y2, 236.33/34.81 Y0))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (subset( 236.33/34.81 Y0, Y1) => 236.33/34.81 (setminus( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))) => 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in(Y2, 236.33/34.81 Y1)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 Y0)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 setminus( 236.33/34.81 Y0, Y1)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 subset( 236.33/34.81 setminus( 236.33/34.81 Y0, Y1), 236.33/34.81 Y0))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (( 236.33/34.81 setminus( 236.33/34.81 Y0, Y1) = 236.33/34.81 emptyset) => 236.33/34.81 subset( 236.33/34.81 Y0, Y1)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $o]: 236.33/34.81 (( 236.33/34.81 in(Y2, 236.33/34.81 Y0) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 Y3)) => 236.33/34.81 (( 236.33/34.81 ( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 ( 236.33/34.81 in(Y2, 236.33/34.81 Y1) => Y3)) => 236.33/34.81 Y3))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (in(Y2, 236.33/34.81 Y1) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y0))) => 236.33/34.81 (( 236.33/34.81 ~( 236.33/34.81 in(Y2, 236.33/34.81 Y1))) => 236.33/34.81 (~( 236.33/34.81 in(Y2, 236.33/34.81 symdiff( 236.33/34.81 Y0, Y1))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y0, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 in(Y1, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)) = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)))) & 236.33/34.81 (setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)) = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y0) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset), 236.33/34.81 Y0)))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 Y0) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset), 236.33/34.81 powerset( 236.33/34.81 Y0))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 setadjoin( 236.33/34.81 Y1, 236.33/34.81 emptyset))) => 236.33/34.81 (( 236.33/34.81 Y2 = Y1) | 236.33/34.81 (Y2 = Y0)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 subset( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 powerset( 236.33/34.81 powerset( 236.33/34.81 binunion( 236.33/34.81 Y0, Y1)))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y1) => 236.33/34.81 in( 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset)), 236.33/34.81 emptyset)), 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) & 236.33/34.81 (??(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 Y1) & 236.33/34.81 (Y2 = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 setadjoin( 236.33/34.81 Y4, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 cartprod( 236.33/34.81 Y0, Y1)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 setunion( 236.33/34.81 Y2)) & 236.33/34.81 (??(( 236.33/34.81 ^[Y4 : $i]: 236.33/34.81 (in(Y4, 236.33/34.81 setunion( 236.33/34.81 Y2)) & 236.33/34.81 (Y2 = 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset), 236.33/34.81 setadjoin( 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 setadjoin( 236.33/34.81 Y4, 236.33/34.81 emptyset)), 236.33/34.81 emptyset))))))))))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i]: 236.33/34.81 (in(Y1, 236.33/34.81 setunion( 236.33/34.81 Y0)) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 in(Y1, 236.33/34.81 Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)), 236.33/34.81 Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 subset( 236.33/34.81 Y0, 236.33/34.81 setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (setunion( 236.33/34.81 setadjoin( 236.33/34.81 Y0, 236.33/34.81 emptyset)) = 236.33/34.81 Y0)))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (!!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y2 = Y3))))))))))) => 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, Y1)) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, Y1) = 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset)))))))))))))) => 236.33/34.81 ( 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (( 236.33/34.81 ??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, Y1)) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, Y1) = 236.33/34.81 setadjoin( 236.33/34.81 Y2, 236.33/34.81 emptyset)))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) & 236.33/34.81 Y1(Y2)))))))))))) => 236.33/34.81 ( 236.33/34.81 !!(( 236.33/34.81 ^[Y0 : $i]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y1 : $i > $o]: 236.33/34.81 (!!(( 236.33/34.81 ^[Y2 : $i]: 236.33/34.81 (in(Y2, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y2) => 236.33/34.81 (( 236.33/34.81 !!(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 Y0) => 236.33/34.81 (Y1(Y3) => 236.33/34.81 (Y3 = Y2)))))) => 236.33/34.81 (??(( 236.33/34.81 ^[Y3 : $i]: 236.33/34.81 (in(Y3, 236.33/34.81 dsetconstr( 236.33/34.81 Y0, Y1)) & 236.33/34.81 (dsetconstr( 236.33/34.81 Y0, Y1) = 236.33/34.81 setadjoin( 236.33/34.81 Y3, 236.33/34.81 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.81 inference('ho_norm', [status(thm)], ['170'])). 236.33/34.81 tff('172', plain, 236.33/34.81 ~ ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, setadjoin(Y0, Y1)) <=> 236.33/34.81 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, powerset(Y0)) <=> 236.33/34.81 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 (in(Y1, setunion(Y0)) <=> 236.33/34.81 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 236.33/34.81 (in(emptyset, omega) => 236.33/34.81 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (((!!((^[Y1 : $i]: 236.33/34.81 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.81 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.81 in(emptyset, Y0)) => 236.33/34.81 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.81 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.81 (!!((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 (??((^[Y3 : $i]: 236.33/34.81 (Y0(Y2, Y3) & 236.33/34.81 (!!((^[Y4 : $i]: 236.33/34.81 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.81 (??((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) <=> 236.33/34.81 (??((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 (in(Y1, Y0) & 236.33/34.81 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (??((^[Y1 : $i]: 236.33/34.81 ((!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y1) => 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.81 ((!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y1) => 236.33/34.81 (in(Y2, Y4) <=> 236.33/34.81 in(Y3, Y4)))))) => 236.33/34.81 (Y2 = Y3)))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.81 ((!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y3) => 236.33/34.81 in(Y4, Y2))))) | 236.33/34.81 (!!((^[Y4 : $i]: 236.33/34.81 (in(Y4, Y2) => 236.33/34.81 in(Y4, Y3)))))))))))))& 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.81 (!!((^[Y3 : $i]: 236.33/34.81 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.81 (??((^[Y3 : $i]: 236.33/34.81 (??((^[Y4 : $i]: 236.33/34.81 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.81 (~((??((^[Y5 : $i]: 236.33/34.81 (in(Y5, Y3) & 236.33/34.81 in(Y5, Y2)))))))& 236.33/34.81 (!!((^[Y5 : $i]: 236.33/34.81 (in(Y5, Y1) => 236.33/34.81 (in(Y4, Y5) | 236.33/34.81 (!!((^[Y6 : $i]: 236.33/34.81 (in(Y6, 236.33/34.81 Y5) => 236.33/34.81 in(Y6, 236.33/34.81 Y3)))))))))))))))))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i > $o]: 236.33/34.81 ((??((^[Y1 : $i]: 236.33/34.81 (Y0(Y1) & 236.33/34.81 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.81 Y0(descr(Y0)))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, Y0) => 236.33/34.81 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, dsetconstr(Y0, Y1)) => 236.33/34.81 in(Y2, Y0))))))))))) => 236.33/34.81 ((!!((^[Y0 : $i]: 236.33/34.81 (!!((^[Y1 : $i > $o]: 236.33/34.81 (!!((^[Y2 : $i]: 236.33/34.81 (in(Y2, dsetconstr(Y0, Y1)) => 236.33/34.81 Y1(Y2))))))))))) => 236.33/34.81 ((!!((^[Y0 : $o]: 236.33/34.81 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.82 (??(Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.82 (Y0 = Y1))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.82 (Y0 = emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.82 (Y0 = emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (in(Y2, 236.33/34.82 dsetconstr(Y0, Y1)) <=> 236.33/34.82 Y1(Y2)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((Y0 != emptyset) => 236.33/34.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (Y1(Y2) => 236.33/34.82 (dsetconstr(Y0, Y1) != 236.33/34.82 emptyset)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.82 (Y0 != emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.82 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, 236.33/34.82 setadjoin(Y0, Y1)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin(Y0, Y1)) => 236.33/34.82 (!!((^[Y3 : $o]: 236.33/34.82 (((Y2 = Y0) => 236.33/34.82 Y3) => 236.33/34.82 ((in(Y2, 236.33/34.82 Y1) => Y3) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin(Y0, 236.33/34.82 Y1)) => 236.33/34.82 (in(Y2, Y1) | 236.33/34.82 (Y2 = Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (dsetconstr(Y0, 236.33/34.82 (^[Y1 : $i]: $true)) = 236.33/34.82 Y0)))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, Y0))))) => 236.33/34.82 in(Y1, powerset(Y0))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 in(emptyset, powerset(Y0))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 in(emptyset, powerset(Y0))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 powerset( 236.33/34.82 Y0)) => 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y1, Y2) => 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 setunion( 236.33/34.82 Y0))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 setunion(Y0)) => 236.33/34.82 (!!((^[Y2 : $o]: 236.33/34.82 ((!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 Y3) => 236.33/34.82 (in(Y3, 236.33/34.82 Y0) => Y2))))) => 236.33/34.82 Y2))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 powerset( 236.33/34.82 setunion(Y0)))))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 ( 236.33/34.82 Y0(Y2) <=> 236.33/34.82 ( 236.33/34.82 Y2 = Y1)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((Y0 != emptyset) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 in(Y1, Y0)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)) => 236.33/34.82 (Y0 = Y1)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((Y0 != Y1) => 236.33/34.82 (~(in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((Y0 = Y1) => 236.33/34.82 in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)) => 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))) => 236.33/34.82 (( 236.33/34.82 Y2 = Y1) | 236.33/34.82 (Y2 = Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))) => 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y1) != 236.33/34.82 emptyset)))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 emptyset) => 236.33/34.82 Y0(Y1)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 ( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 ( 236.33/34.82 Y0 => 236.33/34.82 in( 236.33/34.82 emptyset, 236.33/34.82 prop2set( 236.33/34.82 Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 (Y0 => 236.33/34.82 set2prop( 236.33/34.82 prop2set( 236.33/34.82 Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 ??(Y0)) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2)))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 (Y2 = Y1)))))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y3, 236.33/34.82 Y1)))))))))))))))) => 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) <=> 236.33/34.82 in(Y3, 236.33/34.82 Y1)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 Y1(Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y0(Y3) => 236.33/34.82 (Y2 = Y3))))))))) <=> 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y1(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (setadjoin( 236.33/34.82 Y0, Y2) = 236.33/34.82 setadjoin( 236.33/34.82 Y1, Y3)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (powerset( 236.33/34.82 Y0) = 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (setunion( 236.33/34.82 Y0) = 236.33/34.82 setunion( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 Y1(Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y0(Y3) => 236.33/34.82 (Y2 = Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y1(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))) => 236.33/34.82 (descr( 236.33/34.82 Y0) = 236.33/34.82 descr(Y1))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y4 : $i]: 236.33/34.82 (in(Y4, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y5 : $i]: 236.33/34.82 (in(Y5, 236.33/34.82 Y1) => 236.33/34.82 (( 236.33/34.82 Y4 = Y5) => 236.33/34.82 (Y2(Y4) <=> 236.33/34.82 Y3(Y5))))))))))) => 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y2) = 236.33/34.82 dsetconstr( 236.33/34.82 Y1, Y3)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!( 236.33/34.82 subset( 236.33/34.82 emptyset))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 subset( 236.33/34.82 Y0, Y1))) => 236.33/34.82 (Y0 != Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (Y0 != Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, Y0)))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (subset( 236.33/34.82 Y1, Y2) => 236.33/34.82 subset( 236.33/34.82 Y0, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y2) => 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 in(Y0, 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 (Y0 = Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, 236.33/34.82 emptyset) => 236.33/34.82 (Y0 = 236.33/34.82 emptyset))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 powerset( 236.33/34.82 Y0))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 powerset( 236.33/34.82 Y0)) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 powerset( 236.33/34.82 Y0))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 subset( 236.33/34.82 powerset( 236.33/34.82 Y0), 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 in( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1), 236.33/34.82 powerset( 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 subset( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $o]: 236.33/34.82 (in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y0) => Y3) => 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y1) => Y3) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) | 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y1, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y2, Y0) => 236.33/34.82 (subset( 236.33/34.82 Y2, Y1) => 236.33/34.82 subset( 236.33/34.82 Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y0))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y1) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 Y1))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y0) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (binintersect( 236.33/34.82 Y0, 236.33/34.82 binunion( 236.33/34.82 Y1, Y2)) = 236.33/34.82 binunion( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 binintersect( 236.33/34.82 Y0, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y0))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (setminus( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 setminus( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 setminus( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $o]: 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y0) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 Y3)) => 236.33/34.82 (( 236.33/34.82 ( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 ( 236.33/34.82 in(Y2, 236.33/34.82 Y1) => Y3)) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)) = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)) = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 Y0) => 236.33/34.82 subset( 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset), 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 Y0) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset), 236.33/34.82 powerset( 236.33/34.82 Y0))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))) => 236.33/34.82 (( 236.33/34.82 Y2 = Y1) | 236.33/34.82 (Y2 = Y0)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 subset( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 subset( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 cartprod( 236.33/34.82 Y0, Y1)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 cartprod( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y0) & 236.33/34.82 (??(( 236.33/34.82 ^[Y4 : $i]: 236.33/34.82 (in(Y4, 236.33/34.82 Y1) & 236.33/34.82 (Y2 = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 setadjoin( 236.33/34.82 Y4, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 cartprod( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 setunion( 236.33/34.82 Y2)) & 236.33/34.82 (??(( 236.33/34.82 ^[Y4 : $i]: 236.33/34.82 (in(Y4, 236.33/34.82 setunion( 236.33/34.82 Y2)) & 236.33/34.82 (Y2 = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 setadjoin( 236.33/34.82 Y4, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 setunion( 236.33/34.82 Y0)) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 in(Y1, 236.33/34.82 Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 subset( 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset)), 236.33/34.82 Y0)))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset)))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (setunion( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset)) = 236.33/34.82 Y0)))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y0) => 236.33/34.82 (Y1(Y2) => 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1)) & 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y1) = 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1)) & 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y1) = 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset)))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (Y1(Y2) => 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y0) => 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y3 = Y2)))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1)) & 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y1) = 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.82 inference('lazy_cnf_imply', [status(thm)], ['171'])). 236.33/34.82 tff('173', plain, 236.33/34.82 ~ ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, setadjoin(Y0, Y1)) <=> 236.33/34.82 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, powerset(Y0)) <=> 236.33/34.82 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, setunion(Y0)) <=> 236.33/34.82 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 236.33/34.82 (in(emptyset, omega) => 236.33/34.82 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (((!!((^[Y1 : $i]: 236.33/34.82 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.82 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.82 in(emptyset, Y0)) => 236.33/34.82 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.82 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 (??((^[Y3 : $i]: 236.33/34.82 (Y0(Y2, Y3) & 236.33/34.82 (!!((^[Y4 : $i]: 236.33/34.82 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.82 (??((^[Y2 : $i]: 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 (in(Y3, Y2) <=> 236.33/34.82 (??((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 (in(Y1, Y0) & 236.33/34.82 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.82 ((!!((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y1) => 236.33/34.82 (in(Y2, Y4) <=> 236.33/34.82 in(Y3, Y4)))))) => 236.33/34.82 (Y2 = Y3)))))))))& 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.82 ((!!((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y3) => 236.33/34.82 in(Y4, Y2))))) | 236.33/34.82 (!!((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y2) => 236.33/34.82 in(Y4, Y3)))))))))))))& 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.82 (??((^[Y3 : $i]: 236.33/34.82 (??((^[Y4 : $i]: 236.33/34.82 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.82 (~((??((^[Y5 : $i]: 236.33/34.82 (in(Y5, Y3) & 236.33/34.82 in(Y5, Y2)))))))& 236.33/34.82 (!!((^[Y5 : $i]: 236.33/34.82 (in(Y5, Y1) => 236.33/34.82 (in(Y4, Y5) | 236.33/34.82 (!!((^[Y6 : $i]: 236.33/34.82 (in(Y6, 236.33/34.82 Y5) => 236.33/34.82 in(Y6, 236.33/34.82 Y3)))))))))))))))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.82 Y0(descr(Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, dsetconstr(Y0, Y1)) => 236.33/34.82 in(Y2, Y0))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.82 (??(Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.82 (Y0 = Y1))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.82 (Y0 = emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.82 (Y0 = emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.82 Y1(Y2)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((Y0 != emptyset) => 236.33/34.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (Y1(Y2) => 236.33/34.82 (dsetconstr(Y0, Y1) != 236.33/34.82 emptyset)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.82 (Y0 != emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.82 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, 236.33/34.82 setadjoin(Y0, Y1)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin(Y0, Y1)) => 236.33/34.82 (!!((^[Y3 : $o]: 236.33/34.82 (((Y2 = Y0) => 236.33/34.82 Y3) => 236.33/34.82 ((in(Y2, Y1) => 236.33/34.82 Y3) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin(Y0, Y1)) => 236.33/34.82 (in(Y2, Y1) | 236.33/34.82 (Y2 = Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (dsetconstr(Y0, 236.33/34.82 (^[Y1 : $i]: $true)) = 236.33/34.82 Y0)))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, Y0))))) => 236.33/34.82 in(Y1, powerset(Y0))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 in(emptyset, powerset(Y0))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 in(emptyset, powerset(Y0))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 powerset(Y0)) => 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y1, Y2) => 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 setunion( 236.33/34.82 Y0))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 setunion(Y0)) => 236.33/34.82 (!!((^[Y2 : $o]: 236.33/34.82 ((!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 Y3) => 236.33/34.82 (in(Y3, 236.33/34.82 Y0) => Y2))))) => 236.33/34.82 Y2))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 powerset( 236.33/34.82 setunion(Y0)))))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 ( 236.33/34.82 Y0(Y2) => 236.33/34.82 ( 236.33/34.82 Y1 = Y2))))))))) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 ( 236.33/34.82 Y2 = Y1)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((Y0 != emptyset) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 in(Y1, Y0)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)) => 236.33/34.82 (Y0 = Y1)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((Y0 != Y1) => 236.33/34.82 (~(in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((Y0 = Y1) => 236.33/34.82 in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)) => 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 ( 236.33/34.82 in(Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 Y2 = Y1) | 236.33/34.82 ( 236.33/34.82 Y2 = Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))) => 236.33/34.82 ( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1) != 236.33/34.82 emptyset)))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 emptyset) => 236.33/34.82 Y0(Y1)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 ( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 (Y0 => 236.33/34.82 in( 236.33/34.82 emptyset, 236.33/34.82 prop2set( 236.33/34.82 Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 ( 236.33/34.82 Y0 => 236.33/34.82 set2prop( 236.33/34.82 prop2set( 236.33/34.82 Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(Y0)) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2)))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 (Y2 = Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y3, 236.33/34.82 Y1)))))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) <=> 236.33/34.82 in(Y3, 236.33/34.82 Y1)))))))))))))))) => 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 Y1(Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y0(Y3) => 236.33/34.82 (Y2 = Y3))))))))) <=> 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y1(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (setadjoin( 236.33/34.82 Y0, Y2) = 236.33/34.82 setadjoin( 236.33/34.82 Y1, Y3)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (powerset( 236.33/34.82 Y0) = 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (setunion( 236.33/34.82 Y0) = 236.33/34.82 setunion( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 Y1(Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y0(Y3) => 236.33/34.82 (Y2 = Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y1(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))) => 236.33/34.82 (descr( 236.33/34.82 Y0) = 236.33/34.82 descr(Y1))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y4 : $i]: 236.33/34.82 (in(Y4, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y5 : $i]: 236.33/34.82 (in(Y5, 236.33/34.82 Y1) => 236.33/34.82 (( 236.33/34.82 Y4 = Y5) => 236.33/34.82 (Y2(Y4) <=> 236.33/34.82 Y3(Y5))))))))))) => 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y2) = 236.33/34.82 dsetconstr( 236.33/34.82 Y1, Y3)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!( 236.33/34.82 subset( 236.33/34.82 emptyset))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 subset( 236.33/34.82 Y0, Y1))) => 236.33/34.82 (Y0 != Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (Y0 != Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, Y0)))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (subset( 236.33/34.82 Y1, Y2) => 236.33/34.82 subset( 236.33/34.82 Y0, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y2) => 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 in(Y0, 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 (Y0 = Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, 236.33/34.82 emptyset) => 236.33/34.82 (Y0 = 236.33/34.82 emptyset))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 powerset( 236.33/34.82 Y0))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 powerset( 236.33/34.82 Y0)) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 powerset( 236.33/34.82 Y0))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 subset( 236.33/34.82 powerset( 236.33/34.82 Y0), 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 in( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1), 236.33/34.82 powerset( 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 subset( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $o]: 236.33/34.82 (in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y0) => Y3) => 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y1) => Y3) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) | 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y1, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y2, Y0) => 236.33/34.82 (subset( 236.33/34.82 Y2, Y1) => 236.33/34.82 subset( 236.33/34.82 Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y0))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y1) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 Y1))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y0) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (binintersect( 236.33/34.82 Y0, 236.33/34.82 binunion( 236.33/34.82 Y1, Y2)) = 236.33/34.82 binunion( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 binintersect( 236.33/34.82 Y0, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y0))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (setminus( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 setminus( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 setminus( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $o]: 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y0) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 Y3)) => 236.33/34.82 (( 236.33/34.82 ( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 ( 236.33/34.82 in(Y2, 236.33/34.82 Y1) => Y3)) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 symdiff( 236.33/34.82 Y0, Y1))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)) = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)))) & 236.33/34.82 (setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)) = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 Y0) => 236.33/34.82 subset( 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset), 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 Y0) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset), 236.33/34.82 powerset( 236.33/34.82 Y0))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))) => 236.33/34.82 (( 236.33/34.82 Y2 = Y1) | 236.33/34.82 (Y2 = Y0)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 subset( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 subset( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 powerset( 236.33/34.82 powerset( 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y1) => 236.33/34.82 in( 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset)), 236.33/34.82 emptyset)), 236.33/34.82 cartprod( 236.33/34.82 Y0, Y1)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 cartprod( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y0) & 236.33/34.82 (??(( 236.33/34.82 ^[Y4 : $i]: 236.33/34.82 (in(Y4, 236.33/34.82 Y1) & 236.33/34.82 (Y2 = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 setadjoin( 236.33/34.82 Y4, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 cartprod( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 setunion( 236.33/34.82 Y2)) & 236.33/34.82 (??(( 236.33/34.82 ^[Y4 : $i]: 236.33/34.82 (in(Y4, 236.33/34.82 setunion( 236.33/34.82 Y2)) & 236.33/34.82 (Y2 = 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset), 236.33/34.82 setadjoin( 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 setadjoin( 236.33/34.82 Y4, 236.33/34.82 emptyset)), 236.33/34.82 emptyset))))))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 setunion( 236.33/34.82 Y0)) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 in(Y1, 236.33/34.82 Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 subset( 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset)), 236.33/34.82 Y0)))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 setunion( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset)))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (setunion( 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset)) = 236.33/34.82 Y0)))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y0) => 236.33/34.82 (Y1(Y2) => 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1)) & 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y1) = 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1)) & 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y1) = 236.33/34.82 setadjoin( 236.33/34.82 Y2, 236.33/34.82 emptyset)))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (Y1(Y2) => 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 Y0) => 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y3 = Y2)))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (in(Y3, 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1)) & 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y1) = 236.33/34.82 setadjoin( 236.33/34.82 Y3, 236.33/34.82 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.82 inference('lazy_cnf_imply', [status(thm)], ['172'])). 236.33/34.82 tff('174', plain, 236.33/34.82 ~ ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, powerset(Y0)) <=> 236.33/34.82 (!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, setunion(Y0)) <=> 236.33/34.82 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 236.33/34.82 (in(emptyset, omega) => 236.33/34.82 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (((!!((^[Y1 : $i]: 236.33/34.82 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.82 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.82 in(emptyset, Y0)) => 236.33/34.82 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.82 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 (??((^[Y3 : $i]: 236.33/34.82 (Y0(Y2, Y3) & 236.33/34.82 (!!((^[Y4 : $i]: 236.33/34.82 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.82 (??((^[Y2 : $i]: 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 (in(Y3, Y2) <=> 236.33/34.82 (??((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 (in(Y1, Y0) & 236.33/34.82 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.82 ((!!((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y1) => 236.33/34.82 (in(Y2, Y4) <=> 236.33/34.82 in(Y3, Y4)))))) => 236.33/34.82 (Y2 = Y3)))))))))& 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.82 ((!!((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.82 (!!((^[Y4 : $i]: 236.33/34.82 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.82 (!!((^[Y3 : $i]: 236.33/34.82 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.82 (??((^[Y3 : $i]: 236.33/34.82 (??((^[Y4 : $i]: 236.33/34.82 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.82 (~((??((^[Y5 : $i]: 236.33/34.82 (in(Y5, Y3) & 236.33/34.82 in(Y5, Y2)))))))& 236.33/34.82 (!!((^[Y5 : $i]: 236.33/34.82 (in(Y5, Y1) => 236.33/34.82 (in(Y4, Y5) | 236.33/34.82 (!!((^[Y6 : $i]: 236.33/34.82 ( 236.33/34.82 in(Y6, 236.33/34.82 Y5) => 236.33/34.82 in(Y6, 236.33/34.82 Y3)))))))))))))))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.82 Y0(descr(Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, dsetconstr(Y0, Y1)) => 236.33/34.82 in(Y2, Y0))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.82 (??(Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.82 (Y0 = Y1))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.82 (Y0 = emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.82 (Y0 = emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.82 Y1(Y2)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((Y0 != emptyset) => 236.33/34.82 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 (Y1(Y2) => 236.33/34.82 (dsetconstr(Y0, Y1) != 236.33/34.82 emptyset)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.82 (Y0 != emptyset))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.82 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, 236.33/34.82 setadjoin(Y0, Y1)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin(Y0, Y1)) => 236.33/34.82 (!!((^[Y3 : $o]: 236.33/34.82 (((Y2 = Y0) => 236.33/34.82 Y3) => 236.33/34.82 ((in(Y2, Y1) => 236.33/34.82 Y3) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin(Y0, Y1)) => 236.33/34.82 (in(Y2, Y1) | 236.33/34.82 (Y2 = Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (dsetconstr(Y0, 236.33/34.82 (^[Y1 : $i]: $true)) = 236.33/34.82 Y0)))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((!!((^[Y2 : $i]: 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, Y0))))) => 236.33/34.82 in(Y1, powerset(Y0))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 in(emptyset, powerset(Y0))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 in(emptyset, powerset(Y0))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 powerset(Y0)) => 236.33/34.82 (in(Y2, Y1) => 236.33/34.82 in(Y2, Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (in(Y1, Y2) => 236.33/34.82 (in(Y2, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 setunion( 236.33/34.82 Y0))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, setunion(Y0)) => 236.33/34.82 (!!((^[Y2 : $o]: 236.33/34.82 ((!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 ( 236.33/34.82 in(Y1, 236.33/34.82 Y3) => 236.33/34.82 ( 236.33/34.82 in(Y3, 236.33/34.82 Y0) => Y2))))) => 236.33/34.82 Y2))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y1, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 powerset( 236.33/34.82 setunion(Y0)))))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 ((??((^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 ( 236.33/34.82 Y1 = Y2))))))))) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 (!!((^[Y2 : $i]: 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 (Y2 = Y1)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ((Y0 != emptyset) => 236.33/34.82 (??((^[Y1 : $i]: 236.33/34.82 in(Y1, Y0)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y0, 236.33/34.82 setadjoin(Y1, 236.33/34.82 emptyset)) => 236.33/34.82 (Y0 = Y1)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((Y0 != Y1) => 236.33/34.82 (~(in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ((Y0 = Y1) => 236.33/34.82 in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset)) => 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 Y2 = Y1) | 236.33/34.82 ( 236.33/34.82 Y2 = Y0)))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))) => 236.33/34.82 ( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1) != 236.33/34.82 emptyset)))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 (!!((^[Y1 : $i]: 236.33/34.82 ( 236.33/34.82 in(Y1, 236.33/34.82 emptyset) => 236.33/34.82 Y0(Y1)))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!((^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 ( 236.33/34.82 ~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 (Y0 => 236.33/34.82 in( 236.33/34.82 emptyset, 236.33/34.82 prop2set( 236.33/34.82 Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $o]: 236.33/34.82 (Y0 => 236.33/34.82 set2prop( 236.33/34.82 prop2set( 236.33/34.82 Y0)))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 Y1(Y2))))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 (~( 236.33/34.82 Y1(Y2)))))))))))))) => 236.33/34.82 ((!!((^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(Y0)) => 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2)))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 (Y2 = Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y3, 236.33/34.82 Y1)))))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) <=> 236.33/34.82 in(Y3, 236.33/34.82 Y1)))))))))))))))) => 236.33/34.82 ((!!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 Y1(Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y0(Y3) => 236.33/34.82 (Y2 = Y3))))))))) <=> 236.33/34.82 (??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y1(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (setadjoin( 236.33/34.82 Y0, Y2) = 236.33/34.82 setadjoin( 236.33/34.82 Y1, Y3)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (powerset( 236.33/34.82 Y0) = 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (setunion( 236.33/34.82 Y0) = 236.33/34.82 setunion( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (Y0(Y1) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y1) => 236.33/34.82 (Y0(Y2) => 236.33/34.82 (Y1 = Y2))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (( 236.33/34.82 Y2 = Y3) => 236.33/34.82 (Y0(Y2) <=> 236.33/34.82 Y1(Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y0(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y0(Y3) => 236.33/34.82 (Y2 = Y3))))))))) => 236.33/34.82 (( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (Y1(Y2) & 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i]: 236.33/34.82 (Y1(Y3) => 236.33/34.82 (Y2 = Y3))))))))) => 236.33/34.82 (descr( 236.33/34.82 Y0) = 236.33/34.82 descr(Y1))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i > $o]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $i > $o]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y4 : $i]: 236.33/34.82 (in(Y4, 236.33/34.82 Y0) => 236.33/34.82 (!!(( 236.33/34.82 ^[Y5 : $i]: 236.33/34.82 (in(Y5, 236.33/34.82 Y1) => 236.33/34.82 (( 236.33/34.82 Y4 = Y5) => 236.33/34.82 (Y2(Y4) <=> 236.33/34.82 Y3(Y5))))))))))) => 236.33/34.82 (dsetconstr( 236.33/34.82 Y0, Y2) = 236.33/34.82 dsetconstr( 236.33/34.82 Y1, Y3)))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 Y0 = Y1) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 !!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!( 236.33/34.82 subset( 236.33/34.82 emptyset))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 subset( 236.33/34.82 Y0, Y1))) => 236.33/34.82 (Y0 != Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (Y0 != Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, Y0)))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (subset( 236.33/34.82 Y1, Y2) => 236.33/34.82 subset( 236.33/34.82 Y0, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y2) => 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 in(Y0, 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 (Y0 = Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, 236.33/34.82 emptyset) => 236.33/34.82 (Y0 = 236.33/34.82 emptyset))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 in(Y1, 236.33/34.82 powerset( 236.33/34.82 Y0))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (in(Y1, 236.33/34.82 powerset( 236.33/34.82 Y0)) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 in(Y0, 236.33/34.82 powerset( 236.33/34.82 Y0))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 subset( 236.33/34.82 powerset( 236.33/34.82 Y0), 236.33/34.82 powerset( 236.33/34.82 Y1))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 in( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1), 236.33/34.82 powerset( 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i > $o]: 236.33/34.82 subset( 236.33/34.82 dsetconstr( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 in(Y1, 236.33/34.82 setadjoin( 236.33/34.82 Y0, 236.33/34.82 setadjoin( 236.33/34.82 Y1, 236.33/34.82 emptyset))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y3 : $o]: 236.33/34.82 (in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y0) => Y3) => 236.33/34.82 (( 236.33/34.82 in(Y2, 236.33/34.82 Y1) => Y3) => 236.33/34.82 Y3))))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) | 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y0, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 Y1, 236.33/34.82 binunion( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y2, Y0) => 236.33/34.82 (subset( 236.33/34.82 Y2, Y1) => 236.33/34.82 subset( 236.33/34.82 Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y0))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 Y0))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y1) => 236.33/34.82 subset( 236.33/34.82 Y1, Y0)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 ~(( 236.33/34.82 ??(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) & 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 subset( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 Y1))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y1, Y0) => 236.33/34.82 (binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1) = 236.33/34.82 Y0) => 236.33/34.82 subset( 236.33/34.82 Y0, Y1)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (binintersect( 236.33/34.82 Y0, 236.33/34.82 binunion( 236.33/34.82 Y1, Y2)) = 236.33/34.82 binunion( 236.33/34.82 binintersect( 236.33/34.82 Y0, Y1), 236.33/34.82 binintersect( 236.33/34.82 Y0, Y2)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)) => 236.33/34.82 in(Y2, 236.33/34.82 Y0))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (subset( 236.33/34.82 Y0, Y1) => 236.33/34.82 (setminus( 236.33/34.82 Y0, Y1) = 236.33/34.82 emptyset)))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))) => 236.33/34.82 (in(Y2, 236.33/34.82 Y0) => 236.33/34.82 in(Y2, 236.33/34.82 Y1)))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))) => 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y1))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 Y0)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (( 236.33/34.82 ~( 236.33/34.82 in(Y2, 236.33/34.82 Y0))) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.82 setminus( 236.33/34.82 Y0, Y1)))))))))))))) => 236.33/34.82 ( 236.33/34.82 ( 236.33/34.82 !!(( 236.33/34.82 ^[Y0 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y1 : $i]: 236.33/34.82 (!!(( 236.33/34.82 ^[Y2 : $i]: 236.33/34.82 (in(Y2, 236.33/34.82 Y1) => 236.33/34.82 (~( 236.33/34.82 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 setminus( 236.33/34.83 Y0, Y1), 236.33/34.83 Y0))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 setminus( 236.33/34.83 Y0, Y1) = 236.33/34.83 emptyset) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $o]: 236.33/34.83 (( 236.33/34.83 in(Y2, 236.33/34.83 Y0) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 Y3)) => 236.33/34.83 (( 236.33/34.83 ( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 ( 236.33/34.83 in(Y2, 236.33/34.83 Y1) => Y3)) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)) = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)) = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y0) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset), 236.33/34.83 Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y0) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset), 236.33/34.83 powerset( 236.33/34.83 Y0))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))) => 236.33/34.83 (( 236.33/34.83 Y2 = Y1) | 236.33/34.83 (Y2 = Y0)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) & 236.33/34.83 (??(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 Y1) & 236.33/34.83 (Y2 = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 setadjoin( 236.33/34.83 Y4, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 Y2)) & 236.33/34.83 (??(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 setunion( 236.33/34.83 Y2)) & 236.33/34.83 (Y2 = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 setadjoin( 236.33/34.83 Y4, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 setunion( 236.33/34.83 Y0)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 in(Y1, 236.33/34.83 Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)), 236.33/34.83 Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 Y0, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)) = 236.33/34.83 Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset)))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y3 = Y2)))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.83 inference('lazy_cnf_imply', [status(thm)], ['173'])). 236.33/34.83 tff('175', plain, 236.33/34.83 ~ ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, setunion(Y0)) <=> 236.33/34.83 (??((^[Y2 : $i]: (in(Y1, Y2) & in(Y2, Y0)))))))))))) => 236.33/34.83 (in(emptyset, omega) => 236.33/34.83 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (((!!((^[Y1 : $i]: 236.33/34.83 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.83 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.83 in(emptyset, Y0)) => 236.33/34.83 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.83 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 (??((^[Y3 : $i]: 236.33/34.83 (Y0(Y2, Y3) & 236.33/34.83 (!!((^[Y4 : $i]: 236.33/34.83 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.83 (??((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) <=> 236.33/34.83 (??((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 (in(Y1, Y0) & 236.33/34.83 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.83 ((!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y1) => 236.33/34.83 (in(Y2, Y4) <=> 236.33/34.83 in(Y3, Y4)))))) => 236.33/34.83 (Y2 = Y3)))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.83 ((!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.83 (!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.83 (??((^[Y3 : $i]: 236.33/34.83 (??((^[Y4 : $i]: 236.33/34.83 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.83 (~((??((^[Y5 : $i]: 236.33/34.83 (in(Y5, Y3) & 236.33/34.83 in(Y5, Y2)))))))& 236.33/34.83 (!!((^[Y5 : $i]: 236.33/34.83 (in(Y5, Y1) => 236.33/34.83 (in(Y4, Y5) | 236.33/34.83 (!!((^[Y6 : $i]: 236.33/34.83 (in(Y6, 236.33/34.83 Y5) => 236.33/34.83 in(Y6, 236.33/34.83 Y3)))))))))))))))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.83 Y0(descr(Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) => 236.33/34.83 in(Y2, Y0))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.83 (??(Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.83 (Y0 = Y1))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.83 (Y0 = emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.83 (Y0 = emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.83 Y1(Y2)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((Y0 != emptyset) => 236.33/34.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (dsetconstr(Y0, Y1) != 236.33/34.83 emptyset)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.83 (Y0 != emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.83 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, 236.33/34.83 setadjoin(Y0, Y1)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin(Y0, Y1)) => 236.33/34.83 (!!((^[Y3 : $o]: 236.33/34.83 (((Y2 = Y0) => 236.33/34.83 Y3) => 236.33/34.83 ((in(Y2, Y1) => 236.33/34.83 Y3) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin(Y0, Y1)) => 236.33/34.83 (in(Y2, Y1) | 236.33/34.83 (Y2 = Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (dsetconstr(Y0, 236.33/34.83 (^[Y1 : $i]: $true)) = 236.33/34.83 Y0)))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, Y0))))) => 236.33/34.83 in(Y1, powerset(Y0))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 in(emptyset, powerset(Y0))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 in(emptyset, powerset(Y0))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 powerset(Y0)) => 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y1, Y2) => 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 setunion(Y0))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, setunion(Y0)) => 236.33/34.83 (!!((^[Y2 : $o]: 236.33/34.83 ((!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y3) => 236.33/34.83 ( 236.33/34.83 in(Y3, 236.33/34.83 Y0) => Y2))))) => 236.33/34.83 Y2))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 powerset( 236.33/34.83 setunion(Y0)))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 (Y2 = Y1)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((Y0 != emptyset) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 in(Y1, Y0)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y0, 236.33/34.83 setadjoin(Y1, 236.33/34.83 emptyset)) => 236.33/34.83 (Y0 = Y1)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((Y0 != Y1) => 236.33/34.83 (~(in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((Y0 = Y1) => 236.33/34.83 in(Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)) => 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))) => 236.33/34.83 (( 236.33/34.83 Y2 = Y1) | 236.33/34.83 (Y2 = Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 ((??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))) => 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) != 236.33/34.83 emptyset)))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 emptyset) => 236.33/34.83 Y0(Y1)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 ( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 ( 236.33/34.83 ~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (Y0 => 236.33/34.83 in( 236.33/34.83 emptyset, 236.33/34.83 prop2set( 236.33/34.83 Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (Y0 => 236.33/34.83 set2prop( 236.33/34.83 prop2set( 236.33/34.83 Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(Y0)) => 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 (Y2 = Y1)))))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y3, 236.33/34.83 Y1)))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) <=> 236.33/34.83 in(Y3, 236.33/34.83 Y1)))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 Y1(Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y0(Y3) => 236.33/34.83 (Y2 = Y3))))))))) <=> 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y1(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))))))))))) => 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (setadjoin( 236.33/34.83 Y0, Y2) = 236.33/34.83 setadjoin( 236.33/34.83 Y1, Y3)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (powerset( 236.33/34.83 Y0) = 236.33/34.83 powerset( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (setunion( 236.33/34.83 Y0) = 236.33/34.83 setunion( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 Y1(Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y0(Y3) => 236.33/34.83 (Y2 = Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y1(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))) => 236.33/34.83 (descr( 236.33/34.83 Y0) = 236.33/34.83 descr(Y1))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y5 : $i]: 236.33/34.83 (in(Y5, 236.33/34.83 Y1) => 236.33/34.83 (( 236.33/34.83 Y4 = Y5) => 236.33/34.83 (Y2(Y4) <=> 236.33/34.83 Y3(Y5))))))))))) => 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y2) = 236.33/34.83 dsetconstr( 236.33/34.83 Y1, Y3)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1))))) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 subset( 236.33/34.83 Y1, Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1))))) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!( 236.33/34.83 subset( 236.33/34.83 emptyset))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 Y0)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 subset( 236.33/34.83 Y0, Y1))) => 236.33/34.83 (Y0 != Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (Y0 != Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 Y0, Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (subset( 236.33/34.83 Y1, Y2) => 236.33/34.83 subset( 236.33/34.83 Y0, Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y2) => 236.33/34.83 subset( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 in(Y0, 236.33/34.83 powerset( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (subset( 236.33/34.83 Y1, Y0) => 236.33/34.83 (Y0 = Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, 236.33/34.83 emptyset) => 236.33/34.83 (Y0 = 236.33/34.83 emptyset))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y1, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 powerset( 236.33/34.83 Y0))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 powerset( 236.33/34.83 Y0)) => 236.33/34.83 subset( 236.33/34.83 Y1, Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 powerset( 236.33/34.83 Y0))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 subset( 236.33/34.83 powerset( 236.33/34.83 Y0), 236.33/34.83 powerset( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 in( 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1), 236.33/34.83 powerset( 236.33/34.83 Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 subset( 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1), 236.33/34.83 Y0))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $o]: 236.33/34.83 (in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (( 236.33/34.83 in(Y2, 236.33/34.83 Y0) => Y3) => 236.33/34.83 (( 236.33/34.83 in(Y2, 236.33/34.83 Y1) => Y3) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) | 236.33/34.83 in(Y2, 236.33/34.83 Y0)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 Y0, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 Y1, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 in(Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y2, Y0) => 236.33/34.83 (subset( 236.33/34.83 Y2, Y1) => 236.33/34.83 subset( 236.33/34.83 Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1)) => 236.33/34.83 in(Y2, 236.33/34.83 Y0))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1), 236.33/34.83 Y0))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 Y1, Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1)) => 236.33/34.83 in(Y2, 236.33/34.83 Y1))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 in(Y2, 236.33/34.83 Y1))))))) => 236.33/34.83 (binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 emptyset)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1), 236.33/34.83 Y1))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y1, Y0) => 236.33/34.83 (binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y0) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (binintersect( 236.33/34.83 Y0, 236.33/34.83 binunion( 236.33/34.83 Y1, Y2)) = 236.33/34.83 binunion( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1), 236.33/34.83 binintersect( 236.33/34.83 Y0, Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)) => 236.33/34.83 in(Y2, 236.33/34.83 Y0))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (setminus( 236.33/34.83 Y0, Y1) = 236.33/34.83 emptyset)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 Y0)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 setminus( 236.33/34.83 Y0, Y1), 236.33/34.83 Y0))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 setminus( 236.33/34.83 Y0, Y1) = 236.33/34.83 emptyset) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $o]: 236.33/34.83 (( 236.33/34.83 in(Y2, 236.33/34.83 Y0) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 Y3)) => 236.33/34.83 (( 236.33/34.83 ( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 ( 236.33/34.83 in(Y2, 236.33/34.83 Y1) => Y3)) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)) = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)) = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y0) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset), 236.33/34.83 Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y0) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset), 236.33/34.83 powerset( 236.33/34.83 Y0))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))) => 236.33/34.83 (( 236.33/34.83 Y2 = Y1) | 236.33/34.83 (Y2 = Y0)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) & 236.33/34.83 (??(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 Y1) & 236.33/34.83 (Y2 = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 setadjoin( 236.33/34.83 Y4, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 Y2)) & 236.33/34.83 (??(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 setunion( 236.33/34.83 Y2)) & 236.33/34.83 (Y2 = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 setadjoin( 236.33/34.83 Y4, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 setunion( 236.33/34.83 Y0)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 in(Y1, 236.33/34.83 Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)), 236.33/34.83 Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 Y0, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)) = 236.33/34.83 Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset)))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y3 = Y2)))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.83 inference('lazy_cnf_imply', [status(thm)], ['174'])). 236.33/34.83 tff('176', plain, 236.33/34.83 ~ (in(emptyset, omega) => 236.33/34.83 ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (((!!((^[Y1 : $i]: 236.33/34.83 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.83 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.83 in(emptyset, Y0)) => 236.33/34.83 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.83 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 (??((^[Y3 : $i]: 236.33/34.83 (Y0(Y2, Y3) & 236.33/34.83 (!!((^[Y4 : $i]: 236.33/34.83 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.83 (??((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) <=> 236.33/34.83 (??((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 (in(Y1, Y0) & 236.33/34.83 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.83 ((!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y1) => 236.33/34.83 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 236.33/34.83 (Y2 = Y3)))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.83 ((!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.83 (!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.83 (??((^[Y3 : $i]: 236.33/34.83 (??((^[Y4 : $i]: 236.33/34.83 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.83 (~((??((^[Y5 : $i]: 236.33/34.83 (in(Y5, Y3) & 236.33/34.83 in(Y5, Y2)))))))& 236.33/34.83 (!!((^[Y5 : $i]: 236.33/34.83 (in(Y5, Y1) => 236.33/34.83 (in(Y4, Y5) | 236.33/34.83 (!!((^[Y6 : $i]: 236.33/34.83 (in(Y6, Y5) => 236.33/34.83 in(Y6, Y3)))))))))))))))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.83 Y0(descr(Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.83 (??(Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.83 (Y0 = Y1))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.83 (Y0 = emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.83 (Y0 = emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.83 Y1(Y2)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((Y0 != emptyset) => 236.33/34.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (dsetconstr(Y0, Y1) != 236.33/34.83 emptyset)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.83 (Y0 != emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.83 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, 236.33/34.83 setadjoin(Y0, Y1)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin(Y0, Y1)) => 236.33/34.83 (!!((^[Y3 : $o]: 236.33/34.83 (((Y2 = Y0) => 236.33/34.83 Y3) => 236.33/34.83 ((in(Y2, Y1) => 236.33/34.83 Y3) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin(Y0, Y1)) => 236.33/34.83 (in(Y2, Y1) | 236.33/34.83 (Y2 = Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 236.33/34.83 Y0)))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, Y0))))) => 236.33/34.83 in(Y1, powerset(Y0))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 in(emptyset, powerset(Y0))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 in(emptyset, powerset(Y0))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 powerset(Y0)) => 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y1, Y2) => 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 setunion(Y0))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, setunion(Y0)) => 236.33/34.83 (!!((^[Y2 : $o]: 236.33/34.83 ((!!((^[Y3 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y3) => 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => Y2))))) => 236.33/34.83 Y2))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 powerset( 236.33/34.83 setunion(Y0)))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 (Y2 = Y1)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((Y0 != emptyset) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 in(Y1, Y0)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y0, 236.33/34.83 setadjoin(Y1, 236.33/34.83 emptyset)) => 236.33/34.83 (Y0 = Y1)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((Y0 != Y1) => 236.33/34.83 (~(in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((Y0 = Y1) => 236.33/34.83 in(Y0, 236.33/34.83 setadjoin(Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)) => 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))) => 236.33/34.83 (( 236.33/34.83 Y2 = Y1) | 236.33/34.83 (Y2 = Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 ((??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))) => 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) != 236.33/34.83 emptyset)))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 emptyset) => 236.33/34.83 Y0(Y1)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 ( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 ( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (Y0 => 236.33/34.83 in( 236.33/34.83 emptyset, 236.33/34.83 prop2set( 236.33/34.83 Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (Y0 => 236.33/34.83 set2prop( 236.33/34.83 prop2set( 236.33/34.83 Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ??(Y0)) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 ( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 (Y2 = Y1)))))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y3, 236.33/34.83 Y1)))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) <=> 236.33/34.83 in(Y3, 236.33/34.83 Y1)))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 Y1(Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y0(Y3) => 236.33/34.83 (Y2 = Y3))))))))) <=> 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y1(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (setadjoin( 236.33/34.83 Y0, Y2) = 236.33/34.83 setadjoin( 236.33/34.83 Y1, Y3)))))))))))))))) => 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (powerset( 236.33/34.83 Y0) = 236.33/34.83 powerset( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (setunion( 236.33/34.83 Y0) = 236.33/34.83 setunion( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 Y1(Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y0(Y3) => 236.33/34.83 (Y2 = Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y1(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))) => 236.33/34.83 (descr( 236.33/34.83 Y0) = 236.33/34.83 descr(Y1))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y5 : $i]: 236.33/34.83 (in(Y5, 236.33/34.83 Y1) => 236.33/34.83 (( 236.33/34.83 Y4 = Y5) => 236.33/34.83 (Y2(Y4) <=> 236.33/34.83 Y3(Y5))))))))))) => 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y2) = 236.33/34.83 dsetconstr( 236.33/34.83 Y1, Y3)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1))))) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 subset( 236.33/34.83 Y1, Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1))))) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!( 236.33/34.83 subset( 236.33/34.83 emptyset))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 Y0)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 subset( 236.33/34.83 Y0, Y1))) => 236.33/34.83 (Y0 != Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (Y0 != Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 Y0, Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (subset( 236.33/34.83 Y1, Y2) => 236.33/34.83 subset( 236.33/34.83 Y0, Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y2) => 236.33/34.83 subset( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 in(Y0, 236.33/34.83 powerset( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (subset( 236.33/34.83 Y1, Y0) => 236.33/34.83 (Y0 = Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, 236.33/34.83 emptyset) => 236.33/34.83 (Y0 = 236.33/34.83 emptyset))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y1, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 powerset( 236.33/34.83 Y0))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 powerset( 236.33/34.83 Y0)) => 236.33/34.83 subset( 236.33/34.83 Y1, Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 powerset( 236.33/34.83 Y0))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 subset( 236.33/34.83 powerset( 236.33/34.83 Y0), 236.33/34.83 powerset( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 in( 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1), 236.33/34.83 powerset( 236.33/34.83 Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 subset( 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1), 236.33/34.83 Y0))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $o]: 236.33/34.83 (in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (( 236.33/34.83 in(Y2, 236.33/34.83 Y0) => Y3) => 236.33/34.83 (( 236.33/34.83 in(Y2, 236.33/34.83 Y1) => Y3) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) | 236.33/34.83 in(Y2, 236.33/34.83 Y0)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 Y0, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 Y1, 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 in(Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y2, Y0) => 236.33/34.83 (subset( 236.33/34.83 Y2, Y1) => 236.33/34.83 subset( 236.33/34.83 Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1)) => 236.33/34.83 in(Y2, 236.33/34.83 Y0))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1), 236.33/34.83 Y0))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 Y1, Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1)) => 236.33/34.83 in(Y2, 236.33/34.83 Y1))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 in(Y2, 236.33/34.83 Y1))))))) => 236.33/34.83 (binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 emptyset)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1), 236.33/34.83 Y1))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y1, Y0) => 236.33/34.83 (binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1) = 236.33/34.83 Y0) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (binintersect( 236.33/34.83 Y0, 236.33/34.83 binunion( 236.33/34.83 Y1, Y2)) = 236.33/34.83 binunion( 236.33/34.83 binintersect( 236.33/34.83 Y0, Y1), 236.33/34.83 binintersect( 236.33/34.83 Y0, Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)) => 236.33/34.83 in(Y2, 236.33/34.83 Y0))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (subset( 236.33/34.83 Y0, Y1) => 236.33/34.83 (setminus( 236.33/34.83 Y0, Y1) = 236.33/34.83 emptyset)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y2, 236.33/34.83 Y1)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 Y0)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 setminus( 236.33/34.83 Y0, Y1)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 subset( 236.33/34.83 setminus( 236.33/34.83 Y0, Y1), 236.33/34.83 Y0))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 setminus( 236.33/34.83 Y0, Y1) = 236.33/34.83 emptyset) => 236.33/34.83 subset( 236.33/34.83 Y0, Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $o]: 236.33/34.83 (( 236.33/34.83 in(Y2, 236.33/34.83 Y0) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 Y3)) => 236.33/34.83 (( 236.33/34.83 ( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 ( 236.33/34.83 in(Y2, 236.33/34.83 Y1) => Y3)) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (in(Y2, 236.33/34.83 Y1) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y0))) => 236.33/34.83 (( 236.33/34.83 ~( 236.33/34.83 in(Y2, 236.33/34.83 Y1))) => 236.33/34.83 (~( 236.33/34.83 in(Y2, 236.33/34.83 symdiff( 236.33/34.83 Y0, Y1))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)) = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)))) & 236.33/34.83 (setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)) = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y0) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset), 236.33/34.83 Y0)))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y0) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset), 236.33/34.83 powerset( 236.33/34.83 Y0))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))) => 236.33/34.83 (( 236.33/34.83 Y2 = Y1) | 236.33/34.83 (Y2 = Y0)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 subset( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 powerset( 236.33/34.83 powerset( 236.33/34.83 binunion( 236.33/34.83 Y0, Y1)))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y1) => 236.33/34.83 in( 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)), 236.33/34.83 emptyset)), 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) & 236.33/34.83 (??(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 Y1) & 236.33/34.83 (Y2 = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 setadjoin( 236.33/34.83 Y4, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 cartprod( 236.33/34.83 Y0, Y1)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 setunion( 236.33/34.83 Y2)) & 236.33/34.83 (??(( 236.33/34.83 ^[Y4 : $i]: 236.33/34.83 (in(Y4, 236.33/34.83 setunion( 236.33/34.83 Y2)) & 236.33/34.83 (Y2 = 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset), 236.33/34.83 setadjoin( 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 setadjoin( 236.33/34.83 Y4, 236.33/34.83 emptyset)), 236.33/34.83 emptyset))))))))))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 setunion( 236.33/34.83 Y0)) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 in(Y1, 236.33/34.83 Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)), 236.33/34.83 Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 subset( 236.33/34.83 Y0, 236.33/34.83 setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (setunion( 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset)) = 236.33/34.83 Y0)))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset)))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y2, 236.33/34.83 emptyset)))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2)))))))))))) => 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y3 = Y2)))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (in(Y3, 236.33/34.83 dsetconstr( 236.33/34.83 Y0, Y1)) & 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) = 236.33/34.83 setadjoin( 236.33/34.83 Y3, 236.33/34.83 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.83 inference('lazy_cnf_imply', [status(thm)], ['175'])). 236.33/34.83 tff('177', plain, 236.33/34.83 ~ ((!!((^[Y0 : $i]: (in(Y0, omega) => in(setadjoin(Y0, Y0), omega))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (((!!((^[Y1 : $i]: 236.33/34.83 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.83 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.83 in(emptyset, Y0)) => 236.33/34.83 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.83 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 (??((^[Y3 : $i]: 236.33/34.83 (Y0(Y2, Y3) & 236.33/34.83 (!!((^[Y4 : $i]: 236.33/34.83 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.83 (??((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) <=> 236.33/34.83 (??((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 (in(Y1, Y0) & 236.33/34.83 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.83 ((!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y1) => 236.33/34.83 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 236.33/34.83 (Y2 = Y3)))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.83 ((!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.83 (!!((^[Y4 : $i]: 236.33/34.83 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.83 (!!((^[Y3 : $i]: 236.33/34.83 (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.83 (??((^[Y3 : $i]: 236.33/34.83 (??((^[Y4 : $i]: 236.33/34.83 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.83 (~((??((^[Y5 : $i]: 236.33/34.83 (in(Y5, Y3) & 236.33/34.83 in(Y5, Y2)))))))& 236.33/34.83 (!!((^[Y5 : $i]: 236.33/34.83 (in(Y5, Y1) => 236.33/34.83 (in(Y4, Y5) | 236.33/34.83 (!!((^[Y6 : $i]: 236.33/34.83 (in(Y6, Y5) => 236.33/34.83 in(Y6, Y3)))))))))))))))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.83 Y0(descr(Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.83 (??(Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.83 (Y0 = Y1))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.83 (Y0 = emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.83 (Y0 = emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.83 Y1(Y2)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((Y0 != emptyset) => 236.33/34.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 (Y1(Y2) => 236.33/34.83 (dsetconstr(Y0, Y1) != 236.33/34.83 emptyset)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.83 (Y0 != emptyset))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.83 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin(Y0, Y1)) => 236.33/34.83 (!!((^[Y3 : $o]: 236.33/34.83 (((Y2 = Y0) => Y3) => 236.33/34.83 ((in(Y2, Y1) => 236.33/34.83 Y3) => 236.33/34.83 Y3))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 setadjoin(Y0, Y1)) => 236.33/34.83 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 236.33/34.83 Y0)))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((!!((^[Y2 : $i]: 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, Y0))))) => 236.33/34.83 in(Y1, powerset(Y0))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 in(emptyset, powerset(Y0))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 in(emptyset, powerset(Y0))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 powerset(Y0)) => 236.33/34.83 (in(Y2, Y1) => 236.33/34.83 in(Y2, Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (in(Y1, Y2) => 236.33/34.83 (in(Y2, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 setunion(Y0))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, setunion(Y0)) => 236.33/34.83 (!!((^[Y2 : $o]: 236.33/34.83 ((!!((^[Y3 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 Y3) => 236.33/34.83 (in(Y3, 236.33/34.83 Y0) => Y2))))) => 236.33/34.83 Y2))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, Y0) => 236.33/34.83 in(Y1, 236.33/34.83 powerset( 236.33/34.83 setunion(Y0)))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ((??((^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (??((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 (Y2 = Y1)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 ((Y0 != emptyset) => 236.33/34.83 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y0, 236.33/34.83 setadjoin(Y1, 236.33/34.83 emptyset)) => 236.33/34.83 (Y0 = Y1)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((Y0 != Y1) => 236.33/34.83 (~(in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 emptyset))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 ((Y0 = Y1) => 236.33/34.83 in(Y0, 236.33/34.83 setadjoin(Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y0, 236.33/34.83 setadjoin(Y1, 236.33/34.83 emptyset)) => 236.33/34.83 in(Y1, 236.33/34.83 setadjoin(Y0, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (!!((^[Y2 : $i]: 236.33/34.83 ( 236.33/34.83 in(Y2, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 Y2 = Y1) | 236.33/34.83 ( 236.33/34.83 Y2 = Y0)))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 in(Y1, 236.33/34.83 setadjoin( 236.33/34.83 Y0, 236.33/34.83 setadjoin( 236.33/34.83 Y1, 236.33/34.83 emptyset))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 ((??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 ( 236.33/34.83 in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))) => 236.33/34.83 (dsetconstr( 236.33/34.83 Y0, Y1) != 236.33/34.83 emptyset)))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 (!!((^[Y1 : $i]: 236.33/34.83 (in(Y1, 236.33/34.83 emptyset) => 236.33/34.83 Y0(Y1)))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 ((~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 ( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!((^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (Y0 => 236.33/34.83 in(emptyset, 236.33/34.83 prop2set( 236.33/34.83 Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $o]: 236.33/34.83 (Y0 => 236.33/34.83 set2prop( 236.33/34.83 prop2set( 236.33/34.83 Y0)))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ~(( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ~(( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 Y1(Y2))))))) => 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (in(Y2, 236.33/34.83 Y0) & 236.33/34.83 (~( 236.33/34.83 Y1(Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(Y0)) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 ( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2)))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i > $o]: 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 (Y2 = Y1)))))))) => 236.33/34.83 ( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) => 236.33/34.83 in(Y3, 236.33/34.83 Y1)))))))))))))))) => 236.33/34.83 ((!!((^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (in(Y2, 236.33/34.83 Y0) <=> 236.33/34.83 in(Y3, 236.33/34.83 Y1)))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 Y1(Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y0(Y3) => 236.33/34.83 (Y2 = Y3))))))))) <=> 236.33/34.83 (??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y1(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y1(Y3) => 236.33/34.83 (Y2 = Y3))))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (setadjoin( 236.33/34.83 Y0, Y2) = 236.33/34.83 setadjoin( 236.33/34.83 Y1, Y3)))))))))))))))) => 236.33/34.83 ((!!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (powerset( 236.33/34.83 Y0) = 236.33/34.83 powerset( 236.33/34.83 Y1))))))))) => 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (( 236.33/34.83 Y0 = Y1) => 236.33/34.83 (setunion( 236.33/34.83 Y0) = 236.33/34.83 setunion( 236.33/34.83 Y1))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (Y0(Y1) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))) => 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y1) => 236.33/34.83 (Y0(Y2) => 236.33/34.83 (Y1 = Y2))))))))))))) => 236.33/34.83 ( 236.33/34.83 ( 236.33/34.83 !!(( 236.33/34.83 ^[Y0 : $i > $o]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y1 : $i > $o]: 236.33/34.83 (( 236.33/34.83 !!(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (( 236.33/34.83 Y2 = Y3) => 236.33/34.83 (Y0(Y2) <=> 236.33/34.83 Y1(Y3))))))))) => 236.33/34.83 (( 236.33/34.83 ??(( 236.33/34.83 ^[Y2 : $i]: 236.33/34.83 (Y0(Y2) & 236.33/34.83 (!!(( 236.33/34.83 ^[Y3 : $i]: 236.33/34.83 (Y0(Y3) => 236.33/34.83 (Y2 = Y3))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y1(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))) => 236.33/34.84 (descr( 236.33/34.84 Y0) = 236.33/34.84 descr(Y1))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y5 : $i]: 236.33/34.84 (in(Y5, 236.33/34.84 Y1) => 236.33/34.84 (( 236.33/34.84 Y4 = Y5) => 236.33/34.84 (Y2(Y4) <=> 236.33/34.84 Y3(Y5))))))))))) => 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y2) = 236.33/34.84 dsetconstr( 236.33/34.84 Y1, Y3)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!( 236.33/34.84 subset( 236.33/34.84 emptyset))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 subset( 236.33/34.84 Y0, Y1))) => 236.33/34.84 (Y0 != Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (Y0 != Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (subset( 236.33/34.84 Y1, Y2) => 236.33/34.84 subset( 236.33/34.84 Y0, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y2) => 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 in(Y0, 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 (Y0 = Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, 236.33/34.84 emptyset) => 236.33/34.84 (Y0 = 236.33/34.84 emptyset))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 in(Y1, 236.33/34.84 powerset( 236.33/34.84 Y0))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 powerset( 236.33/34.84 Y0)) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 powerset( 236.33/34.84 Y0))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 subset( 236.33/34.84 powerset( 236.33/34.84 Y0), 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 in( 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1), 236.33/34.84 powerset( 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 subset( 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $o]: 236.33/34.84 (in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y0) => Y3) => 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y1) => Y3) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) | 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y1, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y2, Y0) => 236.33/34.84 (subset( 236.33/34.84 Y2, Y1) => 236.33/34.84 subset( 236.33/34.84 Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y0))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 ~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 Y1))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y0) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (binintersect( 236.33/34.84 Y0, 236.33/34.84 binunion( 236.33/34.84 Y1, Y2)) = 236.33/34.84 binunion( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 binintersect( 236.33/34.84 Y0, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y0))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (setminus( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 setminus( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 setminus( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $o]: 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y0) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 Y3)) => 236.33/34.84 (( 236.33/34.84 ( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 ( 236.33/34.84 in(Y2, 236.33/34.84 Y1) => Y3)) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)) = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)) = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 Y0) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset), 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 Y0) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset), 236.33/34.84 powerset( 236.33/34.84 Y0))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))) => 236.33/34.84 (( 236.33/34.84 Y2 = Y1) | 236.33/34.84 (Y2 = Y0)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) & 236.33/34.84 (??(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 Y1) & 236.33/34.84 (Y2 = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 setadjoin( 236.33/34.84 Y4, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 Y2)) & 236.33/34.84 (??(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 setunion( 236.33/34.84 Y2)) & 236.33/34.84 (Y2 = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 setadjoin( 236.33/34.84 Y4, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 setunion( 236.33/34.84 Y0)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 in(Y1, 236.33/34.84 Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)), 236.33/34.84 Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)) = 236.33/34.84 Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset)))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y3 = Y2)))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.84 inference('lazy_cnf_imply', [status(thm)], ['176'])). 236.33/34.84 tff('178', plain, 236.33/34.84 ~ ((!!((^[Y0 : $i]: 236.33/34.84 (((!!((^[Y1 : $i]: 236.33/34.84 ((in(Y1, Y0) & in(Y1, omega)) => 236.33/34.84 in(setadjoin(Y1, Y1), Y0))))) & 236.33/34.84 in(emptyset, Y0)) => 236.33/34.84 (!!((^[Y1 : $i]: (in(Y1, omega) => in(Y1, Y0))))))))) => 236.33/34.84 ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 (??((^[Y3 : $i]: 236.33/34.84 (Y0(Y2, Y3) & 236.33/34.84 (!!((^[Y4 : $i]: 236.33/34.84 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.84 (??((^[Y2 : $i]: 236.33/34.84 (!!((^[Y3 : $i]: 236.33/34.84 (in(Y3, Y2) <=> 236.33/34.84 (??((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.84 (??((^[Y1 : $i]: 236.33/34.84 (in(Y1, Y0) & 236.33/34.84 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (??((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (!!((^[Y3 : $i]: 236.33/34.84 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.84 ((!!((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y1) => 236.33/34.84 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 236.33/34.84 (Y2 = Y3)))))))))& 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (!!((^[Y3 : $i]: 236.33/34.84 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.84 ((!!((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.84 (!!((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.84 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.84 (??((^[Y3 : $i]: 236.33/34.84 (??((^[Y4 : $i]: 236.33/34.84 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.84 (~((??((^[Y5 : $i]: 236.33/34.84 (in(Y5, Y3) & 236.33/34.84 in(Y5, Y2)))))))& 236.33/34.84 (!!((^[Y5 : $i]: 236.33/34.84 (in(Y5, Y1) => 236.33/34.84 (in(Y4, Y5) | 236.33/34.84 (!!((^[Y6 : $i]: 236.33/34.84 (in(Y6, Y5) => 236.33/34.84 in(Y6, Y3)))))))))))))))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??((^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.84 Y0(descr(Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.84 ((!!((^[Y0 : $o]: 236.33/34.84 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??((^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.84 (??(Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.84 (Y0 = Y1))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.84 (Y0 = emptyset))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.84 (Y0 = emptyset))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.84 Y1(Y2)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((Y0 != emptyset) => 236.33/34.84 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (dsetconstr(Y0, Y1) != 236.33/34.84 emptyset)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.84 (Y0 != emptyset))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.84 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.84 (!!((^[Y3 : $o]: 236.33/34.84 (((Y2 = Y0) => Y3) => 236.33/34.84 ((in(Y2, Y1) => 236.33/34.84 Y3) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setadjoin(Y0, Y1)) => 236.33/34.84 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 236.33/34.84 Y0)))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 in(Y2, Y0))))) => 236.33/34.84 in(Y1, powerset(Y0))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 in(emptyset, powerset(Y0))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 powerset(Y0)) => 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 in(Y2, Y0)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y1, Y2) => 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 in(Y1, 236.33/34.84 setunion(Y0))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y1, setunion(Y0)) => 236.33/34.84 (!!((^[Y2 : $o]: 236.33/34.84 ((!!((^[Y3 : $i]: 236.33/34.84 ( 236.33/34.84 in(Y1, 236.33/34.84 Y3) => 236.33/34.84 ( 236.33/34.84 in(Y3, 236.33/34.84 Y0) => Y2))))) => 236.33/34.84 Y2))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y1, Y0) => 236.33/34.84 in(Y1, 236.33/34.84 powerset( 236.33/34.84 setunion(Y0)))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??((^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 (??((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 (Y2 = Y1)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((Y0 != emptyset) => 236.33/34.84 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y0, 236.33/34.84 setadjoin(Y1, 236.33/34.84 emptyset)) => 236.33/34.84 (Y0 = Y1)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((Y0 != Y1) => 236.33/34.84 (~(in(Y1, 236.33/34.84 setadjoin(Y0, 236.33/34.84 emptyset))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((Y0 = Y1) => 236.33/34.84 in(Y0, 236.33/34.84 setadjoin(Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y0, 236.33/34.84 setadjoin(Y1, 236.33/34.84 emptyset)) => 236.33/34.84 in(Y1, 236.33/34.84 setadjoin(Y0, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 Y2 = Y1) | 236.33/34.84 ( 236.33/34.84 Y2 = Y0)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 setadjoin(Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ((??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))) => 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) != 236.33/34.84 emptyset)))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 emptyset) => 236.33/34.84 Y0(Y1)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ((~(( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 (~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ((!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (~( 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 (~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 (~( 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 ( 236.33/34.84 ~(( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $o]: 236.33/34.84 (Y0 => 236.33/34.84 in(emptyset, 236.33/34.84 prop2set(Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $o]: 236.33/34.84 (Y0 => 236.33/34.84 set2prop( 236.33/34.84 prop2set( 236.33/34.84 Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 ~(( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 ( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 (~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??(Y0)) => 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y1) => 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 ( 236.33/34.84 ??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 (Y2 = Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y3, 236.33/34.84 Y1)))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) <=> 236.33/34.84 in(Y3, 236.33/34.84 Y1)))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y1) => 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 Y1(Y3))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y0(Y3) => 236.33/34.84 (Y2 = Y3))))))))) <=> 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y1(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (setadjoin( 236.33/34.84 Y0, Y2) = 236.33/34.84 setadjoin( 236.33/34.84 Y1, Y3)))))))))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (powerset( 236.33/34.84 Y0) = 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (setunion( 236.33/34.84 Y0) = 236.33/34.84 setunion( 236.33/34.84 Y1))))))))) => 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y1) => 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 Y1(Y3))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y0(Y3) => 236.33/34.84 (Y2 = Y3))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y1(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))) => 236.33/34.84 (descr( 236.33/34.84 Y0) = 236.33/34.84 descr(Y1))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y5 : $i]: 236.33/34.84 (in(Y5, 236.33/34.84 Y1) => 236.33/34.84 (( 236.33/34.84 Y4 = Y5) => 236.33/34.84 (Y2(Y4) <=> 236.33/34.84 Y3(Y5))))))))))) => 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y2) = 236.33/34.84 dsetconstr( 236.33/34.84 Y1, Y3)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!( 236.33/34.84 subset( 236.33/34.84 emptyset))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 subset( 236.33/34.84 Y0, Y1))) => 236.33/34.84 (Y0 != Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (Y0 != Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (subset( 236.33/34.84 Y1, Y2) => 236.33/34.84 subset( 236.33/34.84 Y0, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y2) => 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 in(Y0, 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 (Y0 = Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, 236.33/34.84 emptyset) => 236.33/34.84 (Y0 = 236.33/34.84 emptyset))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 in(Y1, 236.33/34.84 powerset( 236.33/34.84 Y0))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 powerset( 236.33/34.84 Y0)) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 powerset( 236.33/34.84 Y0))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 subset( 236.33/34.84 powerset( 236.33/34.84 Y0), 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 in( 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1), 236.33/34.84 powerset( 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 subset( 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $o]: 236.33/34.84 (in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y0) => Y3) => 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y1) => Y3) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) | 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y1, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y2, Y0) => 236.33/34.84 (subset( 236.33/34.84 Y2, Y1) => 236.33/34.84 subset( 236.33/34.84 Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y0))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 ~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 Y1))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y0) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (binintersect( 236.33/34.84 Y0, 236.33/34.84 binunion( 236.33/34.84 Y1, Y2)) = 236.33/34.84 binunion( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 binintersect( 236.33/34.84 Y0, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y0))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (setminus( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 setminus( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 setminus( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $o]: 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y0) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 Y3)) => 236.33/34.84 (( 236.33/34.84 ( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 ( 236.33/34.84 in(Y2, 236.33/34.84 Y1) => Y3)) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)) = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)) = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 Y0) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset), 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 Y0) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset), 236.33/34.84 powerset( 236.33/34.84 Y0))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))) => 236.33/34.84 (( 236.33/34.84 Y2 = Y1) | 236.33/34.84 (Y2 = Y0)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) & 236.33/34.84 (??(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 Y1) & 236.33/34.84 (Y2 = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 setadjoin( 236.33/34.84 Y4, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 Y2)) & 236.33/34.84 (??(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 setunion( 236.33/34.84 Y2)) & 236.33/34.84 (Y2 = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 setadjoin( 236.33/34.84 Y4, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 setunion( 236.33/34.84 Y0)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 in(Y1, 236.33/34.84 Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)), 236.33/34.84 Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)) = 236.33/34.84 Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset)))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y3 = Y2)))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.84 inference('lazy_cnf_imply', [status(thm)], ['177'])). 236.33/34.84 tff('179', plain, 236.33/34.84 ~ ((!!((^[Y0 : ($i * $i) > $o]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 (??((^[Y3 : $i]: 236.33/34.84 (Y0(Y2, Y3) & 236.33/34.84 (!!((^[Y4 : $i]: 236.33/34.84 (Y0(Y2, Y4) => (Y3 = Y4))))))))))))) => 236.33/34.84 (??((^[Y2 : $i]: 236.33/34.84 (!!((^[Y3 : $i]: 236.33/34.84 (in(Y3, Y2) <=> 236.33/34.84 (??((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y1) & Y0(Y4, Y3))))))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.84 (??((^[Y1 : $i]: 236.33/34.84 (in(Y1, Y0) & 236.33/34.84 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (??((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (!!((^[Y3 : $i]: 236.33/34.84 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.84 ((!!((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y1) => 236.33/34.84 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 236.33/34.84 (Y2 = Y3)))))))))& 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (!!((^[Y3 : $i]: 236.33/34.84 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.84 ((!!((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.84 (!!((^[Y4 : $i]: 236.33/34.84 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.84 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.84 (??((^[Y3 : $i]: 236.33/34.84 (??((^[Y4 : $i]: 236.33/34.84 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.84 (~((??((^[Y5 : $i]: 236.33/34.84 (in(Y5, Y3) & 236.33/34.84 in(Y5, Y2)))))))& 236.33/34.84 (!!((^[Y5 : $i]: 236.33/34.84 (in(Y5, Y1) => 236.33/34.84 (in(Y4, Y5) | 236.33/34.84 (!!((^[Y6 : $i]: 236.33/34.84 (in(Y6, Y5) => 236.33/34.84 in(Y6, Y3)))))))))))))))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??((^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.84 Y0(descr(Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.84 ((!!((^[Y0 : $o]: 236.33/34.84 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??((^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.84 (??(Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.84 (Y0 = Y1))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.84 (Y0 = emptyset))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.84 (Y0 = emptyset))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.84 Y1(Y2)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((Y0 != emptyset) => 236.33/34.84 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (dsetconstr(Y0, Y1) != 236.33/34.84 emptyset)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.84 (Y0 != emptyset))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.84 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.84 (!!((^[Y3 : $o]: 236.33/34.84 (((Y2 = Y0) => Y3) => 236.33/34.84 ((in(Y2, Y1) => Y3) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.84 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 236.33/34.84 Y0)))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 in(Y2, Y0))))) => 236.33/34.84 in(Y1, powerset(Y0))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.84 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y1, powerset(Y0)) => 236.33/34.84 (in(Y2, Y1) => 236.33/34.84 in(Y2, Y0)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y1, Y2) => 236.33/34.84 (in(Y2, Y0) => 236.33/34.84 in(Y1, 236.33/34.84 setunion(Y0))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y1, setunion(Y0)) => 236.33/34.84 (!!((^[Y2 : $o]: 236.33/34.84 ((!!((^[Y3 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 Y3) => 236.33/34.84 ( 236.33/34.84 in(Y3, 236.33/34.84 Y0) => Y2))))) => 236.33/34.84 Y2))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y1, Y0) => 236.33/34.84 in(Y1, 236.33/34.84 powerset(setunion(Y0)))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??((^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 (??((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 (Y2 = Y1)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ((Y0 != emptyset) => 236.33/34.84 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y0, 236.33/34.84 setadjoin(Y1, 236.33/34.84 emptyset)) => 236.33/34.84 (Y0 = Y1)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((Y0 != Y1) => 236.33/34.84 (~(in(Y1, 236.33/34.84 setadjoin(Y0, 236.33/34.84 emptyset))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 ((Y0 = Y1) => 236.33/34.84 in(Y0, 236.33/34.84 setadjoin(Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y0, 236.33/34.84 setadjoin(Y1, 236.33/34.84 emptyset)) => 236.33/34.84 in(Y1, 236.33/34.84 setadjoin(Y0, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (!!((^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))) => 236.33/34.84 (( 236.33/34.84 Y2 = Y1) | 236.33/34.84 ( 236.33/34.84 Y2 = Y0)))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 setadjoin(Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin(Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ((??((^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))) => 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) != 236.33/34.84 emptyset)))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 (!!((^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 emptyset) => 236.33/34.84 Y0(Y1)))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ((~(( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 ( 236.33/34.84 in(Y2, 236.33/34.84 Y0) => 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 ( 236.33/34.84 in(Y2, 236.33/34.84 Y0) & 236.33/34.84 ( 236.33/34.84 ~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ((!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (~( 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 (~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 ((~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 (~( 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 ( 236.33/34.84 ~(( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $o]: 236.33/34.84 (Y0 => 236.33/34.84 in(emptyset, 236.33/34.84 prop2set(Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $o]: 236.33/34.84 (Y0 => 236.33/34.84 set2prop( 236.33/34.84 prop2set(Y0)))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!((^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ~(( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 Y1(Y2))))))) => 236.33/34.84 ( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 (~( 236.33/34.84 Y1(Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??(Y0)) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y1) => 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2)))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 ((??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 (Y2 = Y1)))))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y3, 236.33/34.84 Y1)))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i]: 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) <=> 236.33/34.84 in(Y3, 236.33/34.84 Y1)))))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y1) => 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))))))) => 236.33/34.84 ((!!((^[Y0 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 Y1(Y3))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y0(Y3) => 236.33/34.84 (Y2 = Y3))))))))) <=> 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y1(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (setadjoin( 236.33/34.84 Y0, Y2) = 236.33/34.84 setadjoin( 236.33/34.84 Y1, Y3)))))))))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (powerset( 236.33/34.84 Y0) = 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (setunion( 236.33/34.84 Y0) = 236.33/34.84 setunion( 236.33/34.84 Y1))))))))) => 236.33/34.84 ((!!(( 236.33/34.84 ^[Y0 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (Y0(Y1) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y1) => 236.33/34.84 (Y0(Y2) => 236.33/34.84 (Y1 = Y2))))))))))))) => 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (( 236.33/34.84 Y2 = Y3) => 236.33/34.84 (Y0(Y2) <=> 236.33/34.84 Y1(Y3))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y0(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y0(Y3) => 236.33/34.84 (Y2 = Y3))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (Y1(Y2) & 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))) => 236.33/34.84 (descr( 236.33/34.84 Y0) = 236.33/34.84 descr(Y1))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y5 : $i]: 236.33/34.84 (in(Y5, 236.33/34.84 Y1) => 236.33/34.84 (( 236.33/34.84 Y4 = Y5) => 236.33/34.84 (Y2(Y4) <=> 236.33/34.84 Y3(Y5))))))))))) => 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y2) = 236.33/34.84 dsetconstr( 236.33/34.84 Y1, Y3)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 Y0 = Y1) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!( 236.33/34.84 subset( 236.33/34.84 emptyset))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 subset( 236.33/34.84 Y0, Y1))) => 236.33/34.84 (Y0 != Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (Y0 != Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (subset( 236.33/34.84 Y1, Y2) => 236.33/34.84 subset( 236.33/34.84 Y0, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y2) => 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 in(Y0, 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 (Y0 = Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, 236.33/34.84 emptyset) => 236.33/34.84 (Y0 = 236.33/34.84 emptyset))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 in(Y1, 236.33/34.84 powerset( 236.33/34.84 Y0))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 powerset( 236.33/34.84 Y0)) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 powerset( 236.33/34.84 Y0))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 subset( 236.33/34.84 powerset( 236.33/34.84 Y0), 236.33/34.84 powerset( 236.33/34.84 Y1))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 in( 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1), 236.33/34.84 powerset( 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 subset( 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $o]: 236.33/34.84 (in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y0) => Y3) => 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y1) => Y3) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) | 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 Y1, 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y2, Y0) => 236.33/34.84 (subset( 236.33/34.84 Y2, Y1) => 236.33/34.84 subset( 236.33/34.84 Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y0))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 Y1, Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 ~(( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 Y1))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y1, Y0) => 236.33/34.84 (binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1) = 236.33/34.84 Y0) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (binintersect( 236.33/34.84 Y0, 236.33/34.84 binunion( 236.33/34.84 Y1, Y2)) = 236.33/34.84 binunion( 236.33/34.84 binintersect( 236.33/34.84 Y0, Y1), 236.33/34.84 binintersect( 236.33/34.84 Y0, Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)) => 236.33/34.84 in(Y2, 236.33/34.84 Y0))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (subset( 236.33/34.84 Y0, Y1) => 236.33/34.84 (setminus( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))) => 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in(Y2, 236.33/34.84 Y1)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 Y0)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 setminus( 236.33/34.84 Y0, Y1)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 subset( 236.33/34.84 setminus( 236.33/34.84 Y0, Y1), 236.33/34.84 Y0))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (( 236.33/34.84 setminus( 236.33/34.84 Y0, Y1) = 236.33/34.84 emptyset) => 236.33/34.84 subset( 236.33/34.84 Y0, Y1)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $o]: 236.33/34.84 (( 236.33/34.84 in(Y2, 236.33/34.84 Y0) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 Y3)) => 236.33/34.84 (( 236.33/34.84 ( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 ( 236.33/34.84 in(Y2, 236.33/34.84 Y1) => Y3)) => 236.33/34.84 Y3))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (in(Y2, 236.33/34.84 Y1) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y0))) => 236.33/34.84 (( 236.33/34.84 ~( 236.33/34.84 in(Y2, 236.33/34.84 Y1))) => 236.33/34.84 (~( 236.33/34.84 in(Y2, 236.33/34.84 symdiff( 236.33/34.84 Y0, Y1))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y0, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 in(Y1, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)) = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)))) & 236.33/34.84 (setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)) = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 Y0) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset), 236.33/34.84 Y0)))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 Y0) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset), 236.33/34.84 powerset( 236.33/34.84 Y0))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 setadjoin( 236.33/34.84 Y1, 236.33/34.84 emptyset))) => 236.33/34.84 (( 236.33/34.84 Y2 = Y1) | 236.33/34.84 (Y2 = Y0)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 subset( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 powerset( 236.33/34.84 powerset( 236.33/34.84 binunion( 236.33/34.84 Y0, Y1)))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y1) => 236.33/34.84 in( 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset)), 236.33/34.84 emptyset)), 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) & 236.33/34.84 (??(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 Y1) & 236.33/34.84 (Y2 = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 setadjoin( 236.33/34.84 Y4, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 cartprod( 236.33/34.84 Y0, Y1)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 setunion( 236.33/34.84 Y2)) & 236.33/34.84 (??(( 236.33/34.84 ^[Y4 : $i]: 236.33/34.84 (in(Y4, 236.33/34.84 setunion( 236.33/34.84 Y2)) & 236.33/34.84 (Y2 = 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 emptyset), 236.33/34.84 setadjoin( 236.33/34.84 setadjoin( 236.33/34.84 Y3, 236.33/34.84 setadjoin( 236.33/34.84 Y4, 236.33/34.84 emptyset)), 236.33/34.84 emptyset))))))))))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i]: 236.33/34.84 (in(Y1, 236.33/34.84 setunion( 236.33/34.84 Y0)) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 in(Y1, 236.33/34.84 Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)), 236.33/34.84 Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 subset( 236.33/34.84 Y0, 236.33/34.84 setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (setunion( 236.33/34.84 setadjoin( 236.33/34.84 Y0, 236.33/34.84 emptyset)) = 236.33/34.84 Y0)))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (!!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (Y1(Y3) => 236.33/34.84 (Y2 = Y3))))))))))) => 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset)))))))))))))) => 236.33/34.84 ( 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (( 236.33/34.84 ??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 dsetconstr( 236.33/34.84 Y0, Y1)) & 236.33/34.84 (dsetconstr( 236.33/34.84 Y0, Y1) = 236.33/34.84 setadjoin( 236.33/34.84 Y2, 236.33/34.84 emptyset)))))) => 236.33/34.84 (??(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) & 236.33/34.84 Y1(Y2)))))))))))) => 236.33/34.84 ( 236.33/34.84 !!(( 236.33/34.84 ^[Y0 : $i]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y1 : $i > $o]: 236.33/34.84 (!!(( 236.33/34.84 ^[Y2 : $i]: 236.33/34.84 (in(Y2, 236.33/34.84 Y0) => 236.33/34.84 (Y1(Y2) => 236.33/34.84 (( 236.33/34.84 !!(( 236.33/34.84 ^[Y3 : $i]: 236.33/34.84 (in(Y3, 236.33/34.84 Y0) => 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y3 = Y2)))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1)) & 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) = 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.85 inference('lazy_cnf_imply', [status(thm)], ['178'])). 236.33/34.85 tff('180', plain, 236.33/34.85 ~ ((!!((^[Y0 : $i]: 236.33/34.85 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.85 (??((^[Y1 : $i]: 236.33/34.85 (in(Y1, Y0) & 236.33/34.85 (~((??((^[Y2 : $i]: (in(Y2, Y1) & in(Y2, Y0))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (??((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (!!((^[Y3 : $i]: 236.33/34.85 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.85 ((!!((^[Y4 : $i]: 236.33/34.85 (in(Y4, Y1) => 236.33/34.85 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 236.33/34.85 (Y2 = Y3)))))))))& 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (!!((^[Y3 : $i]: 236.33/34.85 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.85 ((!!((^[Y4 : $i]: 236.33/34.85 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.85 (!!((^[Y4 : $i]: 236.33/34.85 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.85 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.85 (??((^[Y3 : $i]: 236.33/34.85 (??((^[Y4 : $i]: 236.33/34.85 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.85 (~((??((^[Y5 : $i]: 236.33/34.85 (in(Y5, Y3) & 236.33/34.85 in(Y5, Y2)))))))& 236.33/34.85 (!!((^[Y5 : $i]: 236.33/34.85 (in(Y5, Y1) => 236.33/34.85 (in(Y4, Y5) | 236.33/34.85 (!!((^[Y6 : $i]: 236.33/34.85 (in(Y6, Y5) => 236.33/34.85 in(Y6, Y3)))))))))))))))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.85 Y0(descr(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.85 ((!!((^[Y0 : $o]: 236.33/34.85 (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.85 (??(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.85 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.85 (Y0 = Y1))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.85 (Y0 = emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.85 (Y0 = emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.85 Y1(Y2)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((Y0 != emptyset) => 236.33/34.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (Y1(Y2) => 236.33/34.85 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.85 (Y0 != emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.85 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.85 (!!((^[Y3 : $o]: 236.33/34.85 (((Y2 = Y0) => Y3) => 236.33/34.85 ((in(Y2, Y1) => Y3) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.85 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = 236.33/34.85 Y0)))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 in(Y2, Y0))))) => 236.33/34.85 in(Y1, powerset(Y0))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y1, powerset(Y0)) => 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 in(Y2, Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y1, Y2) => 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 in(Y1, 236.33/34.85 setunion(Y0))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, setunion(Y0)) => 236.33/34.85 (!!((^[Y2 : $o]: 236.33/34.85 ((!!((^[Y3 : $i]: 236.33/34.85 (in(Y1, Y3) => 236.33/34.85 (in(Y3, 236.33/34.85 Y0) => Y2))))) => 236.33/34.85 Y2))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, Y0) => 236.33/34.85 in(Y1, 236.33/34.85 powerset(setunion(Y0)))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (??((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 (Y2 = Y1)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((Y0 != emptyset) => 236.33/34.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset)) => 236.33/34.85 (Y0 = Y1)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((Y0 != Y1) => 236.33/34.85 (~(in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 emptyset))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((Y0 = Y1) => 236.33/34.85 in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset)) => 236.33/34.85 in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))) => 236.33/34.85 ((Y2 = Y1) | 236.33/34.85 (Y2 = Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 setadjoin(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((??((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))) => 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) != 236.33/34.85 emptyset)))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 emptyset) => 236.33/34.85 Y0(Y1)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((~((!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 (~( 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (~(( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $o]: 236.33/34.85 (Y0 => 236.33/34.85 in(emptyset, 236.33/34.85 prop2set(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $o]: 236.33/34.85 (Y0 => 236.33/34.85 set2prop( 236.33/34.85 prop2set(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ~(( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??(Y0)) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 (Y2 = Y1)))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y3, 236.33/34.85 Y1)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) <=> 236.33/34.85 in(Y3, 236.33/34.85 Y1)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 ??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 Y1(Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y0(Y3) => 236.33/34.85 (Y2 = Y3))))))))) <=> 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y1(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (setadjoin( 236.33/34.85 Y0, Y2) = 236.33/34.85 setadjoin( 236.33/34.85 Y1, Y3)))))))))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (powerset( 236.33/34.85 Y0) = 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (setunion( 236.33/34.85 Y0) = 236.33/34.85 setunion( 236.33/34.85 Y1))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 Y1(Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y0(Y3) => 236.33/34.85 (Y2 = Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y1(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))) => 236.33/34.85 (descr( 236.33/34.85 Y0) = 236.33/34.85 descr(Y1))))))))))) => 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y4 : $i]: 236.33/34.85 (in(Y4, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y5 : $i]: 236.33/34.85 (in(Y5, 236.33/34.85 Y1) => 236.33/34.85 (( 236.33/34.85 Y4 = Y5) => 236.33/34.85 (Y2(Y4) <=> 236.33/34.85 Y3(Y5))))))))))) => 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y2) = 236.33/34.85 dsetconstr( 236.33/34.85 Y1, Y3)))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!( 236.33/34.85 subset( 236.33/34.85 emptyset))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 subset( 236.33/34.85 Y0, Y1))) => 236.33/34.85 (Y0 != Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (Y0 != Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, Y0)))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (subset( 236.33/34.85 Y1, Y2) => 236.33/34.85 subset( 236.33/34.85 Y0, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y2) => 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 in(Y0, 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 (Y0 = Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, 236.33/34.85 emptyset) => 236.33/34.85 (Y0 = 236.33/34.85 emptyset))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 in(Y1, 236.33/34.85 powerset( 236.33/34.85 Y0))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 powerset( 236.33/34.85 Y0)) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 powerset( 236.33/34.85 Y0))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 subset( 236.33/34.85 powerset( 236.33/34.85 Y0), 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 in( 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1), 236.33/34.85 powerset( 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 subset( 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $o]: 236.33/34.85 (in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => Y3) => 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y1) => Y3) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) | 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y1, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y2, Y0) => 236.33/34.85 (subset( 236.33/34.85 Y2, Y1) => 236.33/34.85 subset( 236.33/34.85 Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y0))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y1) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 ~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 Y1))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y0) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (binintersect( 236.33/34.85 Y0, 236.33/34.85 binunion( 236.33/34.85 Y1, Y2)) = 236.33/34.85 binunion( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 binintersect( 236.33/34.85 Y0, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y0))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (setminus( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 setminus( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 setminus( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $o]: 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 Y3)) => 236.33/34.85 (( 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y1) => Y3)) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)) = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)) = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 Y0) => 236.33/34.85 subset( 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset), 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 Y0) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset), 236.33/34.85 powerset( 236.33/34.85 Y0))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))) => 236.33/34.85 (( 236.33/34.85 Y2 = Y1) | 236.33/34.85 (Y2 = Y0)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 subset( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 subset( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 cartprod( 236.33/34.85 Y0, Y1)))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 cartprod( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y0) & 236.33/34.85 (??(( 236.33/34.85 ^[Y4 : $i]: 236.33/34.85 (in(Y4, 236.33/34.85 Y1) & 236.33/34.85 (Y2 = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 setadjoin( 236.33/34.85 Y4, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 cartprod( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 Y2)) & 236.33/34.85 (??(( 236.33/34.85 ^[Y4 : $i]: 236.33/34.85 (in(Y4, 236.33/34.85 setunion( 236.33/34.85 Y2)) & 236.33/34.85 (Y2 = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 setadjoin( 236.33/34.85 Y4, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 setunion( 236.33/34.85 Y0)) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 in(Y1, 236.33/34.85 Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 subset( 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset)), 236.33/34.85 Y0)))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset)))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (setunion( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset)) = 236.33/34.85 Y0)))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y0) => 236.33/34.85 (Y1(Y2) => 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1)) & 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) = 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1)) & 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) = 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset)))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (Y1(Y2) => 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y0) => 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y3 = Y2)))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1)) & 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) = 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.85 inference('lazy_cnf_imply', [status(thm)], ['179'])). 236.33/34.85 tff('181', plain, 236.33/34.85 ~ ((!!((^[Y0 : $i]: 236.33/34.85 (??((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))))))& 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (!!((^[Y3 : $i]: 236.33/34.85 ((in(Y3, Y0) & in(Y2, Y0)) => 236.33/34.85 ((!!((^[Y4 : $i]: 236.33/34.85 (in(Y4, Y1) => 236.33/34.85 (in(Y2, Y4) <=> in(Y3, Y4)))))) => 236.33/34.85 (Y2 = Y3)))))))))& 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (!!((^[Y3 : $i]: 236.33/34.85 ((in(Y3, Y1) & in(Y2, Y1)) => 236.33/34.85 ((!!((^[Y4 : $i]: 236.33/34.85 (in(Y4, Y3) => in(Y4, Y2))))) | 236.33/34.85 (!!((^[Y4 : $i]: 236.33/34.85 (in(Y4, Y2) => in(Y4, Y3)))))))))))))& 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (((??((^[Y3 : $i]: in(Y3, Y2)))) & 236.33/34.85 (!!((^[Y3 : $i]: (in(Y3, Y2) => in(Y3, Y0)))))) => 236.33/34.85 (??((^[Y3 : $i]: 236.33/34.85 (??((^[Y4 : $i]: 236.33/34.85 (in(Y3, Y1)&in(Y4, Y2)& 236.33/34.85 (~((??((^[Y5 : $i]: 236.33/34.85 (in(Y5, Y3) & 236.33/34.85 in(Y5, Y2)))))))& 236.33/34.85 (!!((^[Y5 : $i]: 236.33/34.85 (in(Y5, Y1) => 236.33/34.85 (in(Y4, Y5) | 236.33/34.85 (!!((^[Y6 : $i]: 236.33/34.85 (in(Y6, Y5) => 236.33/34.85 in(Y6, Y3)))))))))))))))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.85 Y0(descr(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.85 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.85 (??(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.85 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.85 (Y0 = Y1))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.85 (Y0 = emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.85 (Y0 = emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.85 Y1(Y2)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((Y0 != emptyset) => 236.33/34.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (Y1(Y2) => 236.33/34.85 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.85 (Y0 != emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.85 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.85 (!!((^[Y3 : $o]: 236.33/34.85 (((Y2 = Y0) => Y3) => 236.33/34.85 ((in(Y2, Y1) => Y3) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.85 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.85 in(Y1, powerset(Y0))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y1, powerset(Y0)) => 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 in(Y2, Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y1, Y2) => 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 in(Y1, setunion(Y0))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, setunion(Y0)) => 236.33/34.85 (!!((^[Y2 : $o]: 236.33/34.85 ((!!((^[Y3 : $i]: 236.33/34.85 (in(Y1, Y3) => 236.33/34.85 (in(Y3, Y0) => 236.33/34.85 Y2))))) => 236.33/34.85 Y2))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, Y0) => 236.33/34.85 in(Y1, 236.33/34.85 powerset(setunion(Y0)))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (??((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 (Y2 = Y1)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((Y0 != emptyset) => 236.33/34.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset)) => 236.33/34.85 (Y0 = Y1)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((Y0 != Y1) => 236.33/34.85 (~(in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 emptyset))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((Y0 = Y1) => 236.33/34.85 in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset)) => 236.33/34.85 in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))) => 236.33/34.85 ((Y2 = Y1) | 236.33/34.85 (Y2 = Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 setadjoin(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((??((^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))) => 236.33/34.85 (dsetconstr(Y0, 236.33/34.85 Y1) != 236.33/34.85 emptyset)))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 emptyset) => 236.33/34.85 Y0(Y1)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((~((!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (??((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (~((??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 (~( 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (~(( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $o]: 236.33/34.85 (Y0 => 236.33/34.85 in(emptyset, 236.33/34.85 prop2set(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $o]: 236.33/34.85 (Y0 => 236.33/34.85 set2prop( 236.33/34.85 prop2set(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 ~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ~(( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??(Y0)) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 ( 236.33/34.85 Y0(Y1) & 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 (Y2 = Y1)))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 ( 236.33/34.85 Y0(Y1) & 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 Y0 = Y1) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y3, 236.33/34.85 Y1)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) <=> 236.33/34.85 in(Y3, 236.33/34.85 Y1)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 Y1(Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y0(Y3) => 236.33/34.85 (Y2 = Y3))))))))) <=> 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y1(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (setadjoin( 236.33/34.85 Y0, Y2) = 236.33/34.85 setadjoin( 236.33/34.85 Y1, Y3)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (powerset( 236.33/34.85 Y0) = 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (setunion( 236.33/34.85 Y0) = 236.33/34.85 setunion( 236.33/34.85 Y1))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i > $o]: 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 ??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 Y1(Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y0(Y3) => 236.33/34.85 (Y2 = Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y1(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))) => 236.33/34.85 (descr( 236.33/34.85 Y0) = 236.33/34.85 descr(Y1))))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y4 : $i]: 236.33/34.85 (in(Y4, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y5 : $i]: 236.33/34.85 (in(Y5, 236.33/34.85 Y1) => 236.33/34.85 (( 236.33/34.85 Y4 = Y5) => 236.33/34.85 (Y2(Y4) <=> 236.33/34.85 Y3(Y5))))))))))) => 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y2) = 236.33/34.85 dsetconstr( 236.33/34.85 Y1, Y3)))))))))))))))) => 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!( 236.33/34.85 subset( 236.33/34.85 emptyset))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 subset( 236.33/34.85 Y0, Y1))) => 236.33/34.85 (Y0 != Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (Y0 != Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, Y0)))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (subset( 236.33/34.85 Y1, Y2) => 236.33/34.85 subset( 236.33/34.85 Y0, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y2) => 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 in(Y0, 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 (Y0 = Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, 236.33/34.85 emptyset) => 236.33/34.85 (Y0 = 236.33/34.85 emptyset))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 in(Y1, 236.33/34.85 powerset( 236.33/34.85 Y0))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 powerset( 236.33/34.85 Y0)) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 powerset( 236.33/34.85 Y0))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 subset( 236.33/34.85 powerset( 236.33/34.85 Y0), 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 in( 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1), 236.33/34.85 powerset( 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 subset( 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $o]: 236.33/34.85 (in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => Y3) => 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y1) => Y3) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) | 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y1, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y2, Y0) => 236.33/34.85 (subset( 236.33/34.85 Y2, Y1) => 236.33/34.85 subset( 236.33/34.85 Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y0))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y1) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 ~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 Y1))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y0) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (binintersect( 236.33/34.85 Y0, 236.33/34.85 binunion( 236.33/34.85 Y1, Y2)) = 236.33/34.85 binunion( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 binintersect( 236.33/34.85 Y0, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y0))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (setminus( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 setminus( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 setminus( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $o]: 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 Y3)) => 236.33/34.85 (( 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y1) => Y3)) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)) = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)) = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 Y0) => 236.33/34.85 subset( 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset), 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 Y0) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset), 236.33/34.85 powerset( 236.33/34.85 Y0))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))) => 236.33/34.85 (( 236.33/34.85 Y2 = Y1) | 236.33/34.85 (Y2 = Y0)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 subset( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 subset( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 powerset( 236.33/34.85 powerset( 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y1) => 236.33/34.85 in( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)), 236.33/34.85 cartprod( 236.33/34.85 Y0, Y1)))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 cartprod( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y0) & 236.33/34.85 (??(( 236.33/34.85 ^[Y4 : $i]: 236.33/34.85 (in(Y4, 236.33/34.85 Y1) & 236.33/34.85 (Y2 = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 setadjoin( 236.33/34.85 Y4, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 cartprod( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 Y2)) & 236.33/34.85 (??(( 236.33/34.85 ^[Y4 : $i]: 236.33/34.85 (in(Y4, 236.33/34.85 setunion( 236.33/34.85 Y2)) & 236.33/34.85 (Y2 = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 setadjoin( 236.33/34.85 Y4, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 setunion( 236.33/34.85 Y0)) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 in(Y1, 236.33/34.85 Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 subset( 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset)), 236.33/34.85 Y0)))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset)))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (setunion( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset)) = 236.33/34.85 Y0)))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y0) => 236.33/34.85 (Y1(Y2) => 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1)) & 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) = 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1)) & 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) = 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset)))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (Y1(Y2) => 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 Y0) => 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y3 = Y2)))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1)) & 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y1) = 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.85 inference('lazy_cnf_imply', [status(thm)], ['180'])). 236.33/34.85 tff('182', plain, 236.33/34.85 ~ ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.85 Y0(descr(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.85 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.85 (??(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.85 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.85 (Y0 = Y1))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.85 (Y0 = emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.85 (Y0 = emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.85 Y1(Y2)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((Y0 != emptyset) => 236.33/34.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 (Y1(Y2) => 236.33/34.85 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.85 (Y0 != emptyset))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.85 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.85 (!!((^[Y3 : $o]: 236.33/34.85 (((Y2 = Y0) => Y3) => 236.33/34.85 ((in(Y2, Y1) => Y3) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.85 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.85 in(Y1, powerset(Y0))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.85 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y1, powerset(Y0)) => 236.33/34.85 (in(Y2, Y1) => 236.33/34.85 in(Y2, Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y1, Y2) => 236.33/34.85 (in(Y2, Y0) => 236.33/34.85 in(Y1, setunion(Y0))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, setunion(Y0)) => 236.33/34.85 (!!((^[Y2 : $o]: 236.33/34.85 ((!!((^[Y3 : $i]: 236.33/34.85 (in(Y1, Y3) => 236.33/34.85 (in(Y3, Y0) => 236.33/34.85 Y2))))) => 236.33/34.85 Y2))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, Y0) => 236.33/34.85 in(Y1, 236.33/34.85 powerset(setunion(Y0)))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??((^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (??((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 (Y2 = Y1)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ((Y0 != emptyset) => 236.33/34.85 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset)) => 236.33/34.85 (Y0 = Y1)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((Y0 != Y1) => 236.33/34.85 (~(in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 emptyset))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 ((Y0 = Y1) => 236.33/34.85 in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset)) => 236.33/34.85 in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))) => 236.33/34.85 ((Y2 = Y1) | 236.33/34.85 (Y2 = Y0)))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 setadjoin(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin(Y0, 236.33/34.85 setadjoin(Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((??((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))) => 236.33/34.85 (dsetconstr(Y0, 236.33/34.85 Y1) != 236.33/34.85 emptyset)))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 (!!((^[Y1 : $i]: 236.33/34.85 (in(Y1, emptyset) => 236.33/34.85 Y0(Y1)))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((~((!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (??((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((!!((^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (~( 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (~((??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((~((??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ((??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) & 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 (~(( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $o]: 236.33/34.85 (Y0 => 236.33/34.85 in(emptyset, 236.33/34.85 prop2set(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $o]: 236.33/34.85 (Y0 => 236.33/34.85 set2prop( 236.33/34.85 prop2set(Y0)))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!((^[Y1 : $i > $o]: 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 ~(( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 Y1(Y2))))))) => 236.33/34.85 ( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 (~( 236.33/34.85 Y1(Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??(Y0)) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2)))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 (Y2 = Y1)))))))) => 236.33/34.85 (??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y3, 236.33/34.85 Y1)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 Y0 = Y1) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) <=> 236.33/34.85 in(Y3, 236.33/34.85 Y1)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 ((??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 Y1(Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y0(Y3) => 236.33/34.85 (Y2 = Y3))))))))) <=> 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y1(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (setadjoin( 236.33/34.85 Y0, Y2) = 236.33/34.85 setadjoin( 236.33/34.85 Y1, Y3)))))))))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (powerset( 236.33/34.85 Y0) = 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ((!!((^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (setunion( 236.33/34.85 Y0) = 236.33/34.85 setunion( 236.33/34.85 Y1))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i > $o]: 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (Y0(Y1) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))) => 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y1) => 236.33/34.85 (Y0(Y2) => 236.33/34.85 (Y1 = Y2))))))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i > $o]: 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (( 236.33/34.85 Y2 = Y3) => 236.33/34.85 (Y0(Y2) <=> 236.33/34.85 Y1(Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y0(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y0(Y3) => 236.33/34.85 (Y2 = Y3))))))))) => 236.33/34.85 (( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (Y1(Y2) & 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (Y1(Y3) => 236.33/34.85 (Y2 = Y3))))))))) => 236.33/34.85 (descr( 236.33/34.85 Y0) = 236.33/34.85 descr(Y1))))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i > $o]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $i > $o]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y4 : $i]: 236.33/34.85 (in(Y4, 236.33/34.85 Y0) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y5 : $i]: 236.33/34.85 (in(Y5, 236.33/34.85 Y1) => 236.33/34.85 (( 236.33/34.85 Y4 = Y5) => 236.33/34.85 (Y2(Y4) <=> 236.33/34.85 Y3(Y5))))))))))) => 236.33/34.85 (dsetconstr( 236.33/34.85 Y0, Y2) = 236.33/34.85 dsetconstr( 236.33/34.85 Y1, Y3)))))))))))))))) => 236.33/34.85 ((!!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 Y0 = Y1) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 !!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!( 236.33/34.85 subset( 236.33/34.85 emptyset))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 subset( 236.33/34.85 Y0, Y1))) => 236.33/34.85 (Y0 != Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (Y0 != Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, Y0)))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (subset( 236.33/34.85 Y1, Y2) => 236.33/34.85 subset( 236.33/34.85 Y0, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y2) => 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 in(Y0, 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 (Y0 = Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, 236.33/34.85 emptyset) => 236.33/34.85 (Y0 = 236.33/34.85 emptyset))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 in(Y1, 236.33/34.85 powerset( 236.33/34.85 Y0))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 powerset( 236.33/34.85 Y0)) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 powerset( 236.33/34.85 Y0))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 subset( 236.33/34.85 powerset( 236.33/34.85 Y0), 236.33/34.85 powerset( 236.33/34.85 Y1))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 in( 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1), 236.33/34.85 powerset( 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i > $o]: 236.33/34.85 subset( 236.33/34.85 dsetconstr( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $o]: 236.33/34.85 (in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => Y3) => 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y1) => Y3) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) | 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y0, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 Y1, 236.33/34.85 binunion( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y2, Y0) => 236.33/34.85 (subset( 236.33/34.85 Y2, Y1) => 236.33/34.85 subset( 236.33/34.85 Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y0))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y1) => 236.33/34.85 subset( 236.33/34.85 Y1, Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 ~(( 236.33/34.85 ??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) & 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 Y1))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y1, Y0) => 236.33/34.85 (binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1) = 236.33/34.85 Y0) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (binintersect( 236.33/34.85 Y0, 236.33/34.85 binunion( 236.33/34.85 Y1, Y2)) = 236.33/34.85 binunion( 236.33/34.85 binintersect( 236.33/34.85 Y0, Y1), 236.33/34.85 binintersect( 236.33/34.85 Y0, Y2)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)) => 236.33/34.85 in(Y2, 236.33/34.85 Y0))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (subset( 236.33/34.85 Y0, Y1) => 236.33/34.85 (setminus( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))) => 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 in(Y2, 236.33/34.85 Y1)))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 Y0)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 setminus( 236.33/34.85 Y0, Y1)))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 subset( 236.33/34.85 setminus( 236.33/34.85 Y0, Y1), 236.33/34.85 Y0))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (( 236.33/34.85 setminus( 236.33/34.85 Y0, Y1) = 236.33/34.85 emptyset) => 236.33/34.85 subset( 236.33/34.85 Y0, Y1)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1)) => 236.33/34.85 (!!(( 236.33/34.85 ^[Y3 : $o]: 236.33/34.85 (( 236.33/34.85 in(Y2, 236.33/34.85 Y0) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 Y3)) => 236.33/34.85 (( 236.33/34.85 ( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 ( 236.33/34.85 in(Y2, 236.33/34.85 Y1) => Y3)) => 236.33/34.85 Y3))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 Y0) => 236.33/34.85 (in(Y2, 236.33/34.85 Y1) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y0))) => 236.33/34.85 (( 236.33/34.85 ~( 236.33/34.85 in(Y2, 236.33/34.85 Y1))) => 236.33/34.85 (~( 236.33/34.85 in(Y2, 236.33/34.85 symdiff( 236.33/34.85 Y0, Y1))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y0, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 in(Y1, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)) = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (??(( 236.33/34.85 ^[Y2 : $i]: 236.33/34.85 (in(Y2, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (??(( 236.33/34.85 ^[Y3 : $i]: 236.33/34.85 (in(Y3, 236.33/34.85 setunion( 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)))) & 236.33/34.85 (setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y0, 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset)), 236.33/34.85 emptyset)) = 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 emptyset), 236.33/34.85 setadjoin( 236.33/34.85 setadjoin( 236.33/34.85 Y2, 236.33/34.85 setadjoin( 236.33/34.85 Y3, 236.33/34.85 emptyset)), 236.33/34.85 emptyset))))))))))))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 Y0) => 236.33/34.85 subset( 236.33/34.85 setadjoin( 236.33/34.85 Y1, 236.33/34.85 emptyset), 236.33/34.85 Y0)))))))) => 236.33/34.85 ( 236.33/34.85 ( 236.33/34.85 !!(( 236.33/34.85 ^[Y0 : $i]: 236.33/34.85 (!!(( 236.33/34.85 ^[Y1 : $i]: 236.33/34.85 (in(Y1, 236.33/34.85 Y0) => 236.33/34.85 in( 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset), 236.33/34.86 powerset( 236.33/34.86 Y0))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset))) => 236.33/34.86 (( 236.33/34.86 Y2 = Y1) | 236.33/34.86 (Y2 = Y0)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 subset( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 subset( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 cartprod( 236.33/34.86 Y0, Y1)))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 cartprod( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y0) & 236.33/34.86 (??(( 236.33/34.86 ^[Y4 : $i]: 236.33/34.86 (in(Y4, 236.33/34.86 Y1) & 236.33/34.86 (Y2 = 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 setadjoin( 236.33/34.86 Y4, 236.33/34.86 emptyset)), 236.33/34.86 emptyset))))))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 cartprod( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 setunion( 236.33/34.86 Y2)) & 236.33/34.86 (??(( 236.33/34.86 ^[Y4 : $i]: 236.33/34.86 (in(Y4, 236.33/34.86 setunion( 236.33/34.86 Y2)) & 236.33/34.86 (Y2 = 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 setadjoin( 236.33/34.86 Y4, 236.33/34.86 emptyset)), 236.33/34.86 emptyset))))))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (in(Y1, 236.33/34.86 setunion( 236.33/34.86 Y0)) => 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 in(Y1, 236.33/34.86 Y2)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 subset( 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset)), 236.33/34.86 Y0)))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 subset( 236.33/34.86 Y0, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset)))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (setunion( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset)) = 236.33/34.86 Y0)))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y0) => 236.33/34.86 (Y1(Y2) => 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y2 = Y3))))))))))) => 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2))))) => 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1)) & 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y1) = 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1)) & 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y1) = 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset)))))) => 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2)))))))))))) => 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (Y1(Y2) => 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y0) => 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y3 = Y2)))))) => 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1)) & 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y1) = 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.86 inference('lazy_cnf_imply', [status(thm)], ['181'])). 236.33/34.86 tff('183', plain, 236.33/34.86 ~ ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y0) => 236.33/34.86 (Y1(Y2) => in(Y2, dsetconstr(Y0, Y1))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.86 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.86 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.86 (??(Y0)))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.86 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.86 (Y0 = Y1))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.86 (Y0 = emptyset))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.86 (Y0 = emptyset))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y0) => 236.33/34.86 (in(Y2, dsetconstr(Y0, Y1)) <=> 236.33/34.86 Y1(Y2)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y0) => 236.33/34.86 (Y1(Y2) => 236.33/34.86 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.86 (Y0 != emptyset))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.86 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y1) => 236.33/34.86 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.86 (!!((^[Y3 : $o]: 236.33/34.86 (((Y2 = Y0) => Y3) => 236.33/34.86 ((in(Y2, Y1) => Y3) => 236.33/34.86 Y3))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.86 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.86 in(Y1, powerset(Y0))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y1, powerset(Y0)) => 236.33/34.86 (in(Y2, Y1) => 236.33/34.86 in(Y2, Y0)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y1, Y2) => 236.33/34.86 (in(Y2, Y0) => 236.33/34.86 in(Y1, setunion(Y0))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y1, setunion(Y0)) => 236.33/34.86 (!!((^[Y2 : $o]: 236.33/34.86 ((!!((^[Y3 : $i]: 236.33/34.86 (in(Y1, Y3) => 236.33/34.86 (in(Y3, Y0) => 236.33/34.86 Y2))))) => 236.33/34.86 Y2))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y1, Y0) => 236.33/34.86 in(Y1, 236.33/34.86 powerset(setunion(Y0)))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))) => 236.33/34.86 (??((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (Y0(Y2) <=> 236.33/34.86 (Y2 = Y1)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((Y0 != emptyset) => 236.33/34.86 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y0, 236.33/34.86 setadjoin(Y1, emptyset)) => 236.33/34.86 (Y0 = Y1)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((Y0 != Y1) => 236.33/34.86 (~(in(Y1, 236.33/34.86 setadjoin(Y0, 236.33/34.86 emptyset))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((Y0 = Y1) => 236.33/34.86 in(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset)) => 236.33/34.86 in(Y1, 236.33/34.86 setadjoin(Y0, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset))) => 236.33/34.86 ((Y2 = Y1) | 236.33/34.86 (Y2 = Y0)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 in(Y0, 236.33/34.86 setadjoin(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 in(Y1, 236.33/34.86 setadjoin(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((??((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y0) & 236.33/34.86 Y1(Y2))))) => 236.33/34.86 (dsetconstr(Y0, 236.33/34.86 Y1) != 236.33/34.86 emptyset)))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y1, emptyset) => 236.33/34.86 Y0(Y1)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((~((!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (??((^[Y2 : $i]: 236.33/34.86 ( 236.33/34.86 in(Y2, 236.33/34.86 Y0) & 236.33/34.86 ( 236.33/34.86 ~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (~( 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (~((??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 ( 236.33/34.86 in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((~((??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 ( 236.33/34.86 ~( 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (~((!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $o]: 236.33/34.86 (Y0 => 236.33/34.86 in(emptyset, 236.33/34.86 prop2set(Y0)))))) => 236.33/34.86 ((!!((^[Y0 : $o]: 236.33/34.86 (Y0 => 236.33/34.86 set2prop( 236.33/34.86 prop2set(Y0)))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((~(( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 ~(( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 ( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 (~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??(Y0)) => 236.33/34.86 ((!!((^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y1) => 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))) => 236.33/34.86 (??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??((^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) <=> 236.33/34.86 (Y2 = Y1)))))))) => 236.33/34.86 (??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y3, 236.33/34.86 Y1)))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (in(Y2, 236.33/34.86 Y0) <=> 236.33/34.86 in(Y3, 236.33/34.86 Y1)))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y1) => 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (Y0(Y2) <=> 236.33/34.86 Y1(Y3))))))))) => 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y0(Y3) => 236.33/34.86 (Y2 = Y3))))))))) <=> 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y1(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y2 = Y3))))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (setadjoin( 236.33/34.86 Y0, Y2) = 236.33/34.86 setadjoin( 236.33/34.86 Y1, Y3)))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (powerset( 236.33/34.86 Y0) = 236.33/34.86 powerset( 236.33/34.86 Y1))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (setunion( 236.33/34.86 Y0) = 236.33/34.86 setunion( 236.33/34.86 Y1))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y1) => 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (Y0(Y2) <=> 236.33/34.86 Y1(Y3))))))))) => 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y0(Y3) => 236.33/34.86 (Y2 = Y3))))))))) => 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y1(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y2 = Y3))))))))) => 236.33/34.86 (descr( 236.33/34.86 Y0) = 236.33/34.86 descr(Y1))))))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i > $o]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y4 : $i]: 236.33/34.86 (in(Y4, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y5 : $i]: 236.33/34.86 (in(Y5, 236.33/34.86 Y1) => 236.33/34.86 (( 236.33/34.86 Y4 = Y5) => 236.33/34.86 (Y2(Y4) <=> 236.33/34.86 Y3(Y5))))))))))) => 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y2) = 236.33/34.86 dsetconstr( 236.33/34.86 Y1, Y3)))))))))))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 Y1))))) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 subset( 236.33/34.86 Y1, Y0)))))))) => 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 Y1))))) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!( 236.33/34.86 subset( 236.33/34.86 emptyset))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 Y1)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 Y0)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 (~( 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 subset( 236.33/34.86 Y0, Y1))) => 236.33/34.86 (Y0 != Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 (Y0 != Y1)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 subset( 236.33/34.86 Y0, Y0)))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (subset( 236.33/34.86 Y1, Y2) => 236.33/34.86 subset( 236.33/34.86 Y0, Y2)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 subset( 236.33/34.86 Y1, 236.33/34.86 setadjoin( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y2) => 236.33/34.86 subset( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, Y2)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 in(Y0, 236.33/34.86 powerset( 236.33/34.86 Y1))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (subset( 236.33/34.86 Y1, Y0) => 236.33/34.86 (Y0 = Y1))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, 236.33/34.86 emptyset) => 236.33/34.86 (Y0 = 236.33/34.86 emptyset))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y1, Y0) => 236.33/34.86 in(Y1, 236.33/34.86 powerset( 236.33/34.86 Y0))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (in(Y1, 236.33/34.86 powerset( 236.33/34.86 Y0)) => 236.33/34.86 subset( 236.33/34.86 Y1, Y0)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 in(Y0, 236.33/34.86 powerset( 236.33/34.86 Y0))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 subset( 236.33/34.86 powerset( 236.33/34.86 Y0), 236.33/34.86 powerset( 236.33/34.86 Y1))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 in( 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1), 236.33/34.86 powerset( 236.33/34.86 Y0)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 subset( 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1), 236.33/34.86 Y0))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 in(Y1, 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y1) => 236.33/34.86 in(Y2, 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $o]: 236.33/34.86 (in(Y2, 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (( 236.33/34.86 in(Y2, 236.33/34.86 Y0) => Y3) => 236.33/34.86 (( 236.33/34.86 in(Y2, 236.33/34.86 Y1) => Y3) => 236.33/34.86 Y3))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (in(Y2, 236.33/34.86 Y1) | 236.33/34.86 in(Y2, 236.33/34.86 Y0)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 subset( 236.33/34.86 Y0, 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 subset( 236.33/34.86 Y1, 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (in(Y2, 236.33/34.86 Y1) => 236.33/34.86 in(Y2, 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y2, Y0) => 236.33/34.86 (subset( 236.33/34.86 Y2, Y1) => 236.33/34.86 subset( 236.33/34.86 Y2, 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1)) => 236.33/34.86 in(Y2, 236.33/34.86 Y0))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 subset( 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1), 236.33/34.86 Y0))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (binintersect( 236.33/34.86 Y0, Y1) = 236.33/34.86 Y0)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1) = 236.33/34.86 Y1) => 236.33/34.86 subset( 236.33/34.86 Y1, Y0)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1)) => 236.33/34.86 in(Y2, 236.33/34.86 Y1))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 ~(( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 in(Y2, 236.33/34.86 Y1))))))) => 236.33/34.86 (binintersect( 236.33/34.86 Y0, Y1) = 236.33/34.86 emptyset)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 subset( 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1), 236.33/34.86 Y1))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y1, Y0) => 236.33/34.86 (binintersect( 236.33/34.86 Y0, Y1) = 236.33/34.86 Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1) = 236.33/34.86 Y0) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (binintersect( 236.33/34.86 Y0, 236.33/34.86 binunion( 236.33/34.86 Y1, Y2)) = 236.33/34.86 binunion( 236.33/34.86 binintersect( 236.33/34.86 Y0, Y1), 236.33/34.86 binintersect( 236.33/34.86 Y0, Y2)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 in(Y2, 236.33/34.86 setminus( 236.33/34.86 Y0, Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setminus( 236.33/34.86 Y0, Y1)) => 236.33/34.86 in(Y2, 236.33/34.86 Y0))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setminus( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (setminus( 236.33/34.86 Y0, Y1) = 236.33/34.86 emptyset)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 setminus( 236.33/34.86 Y0, Y1)))) => 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 Y1)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 setminus( 236.33/34.86 Y0, Y1)))) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 Y0)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y0))) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 setminus( 236.33/34.86 Y0, Y1)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y1) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 setminus( 236.33/34.86 Y0, Y1)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 subset( 236.33/34.86 setminus( 236.33/34.86 Y0, Y1), 236.33/34.86 Y0))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 setminus( 236.33/34.86 Y0, Y1) = 236.33/34.86 emptyset) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 symdiff( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $o]: 236.33/34.86 (( 236.33/34.86 in(Y2, 236.33/34.86 Y0) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 Y3)) => 236.33/34.86 (( 236.33/34.86 ( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y0))) => 236.33/34.86 ( 236.33/34.86 in(Y2, 236.33/34.86 Y1) => Y3)) => 236.33/34.86 Y3))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 in(Y2, 236.33/34.86 symdiff( 236.33/34.86 Y0, Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y0))) => 236.33/34.86 (in(Y2, 236.33/34.86 Y1) => 236.33/34.86 in(Y2, 236.33/34.86 symdiff( 236.33/34.86 Y0, Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (in(Y2, 236.33/34.86 Y1) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 symdiff( 236.33/34.86 Y0, Y1))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y0))) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 symdiff( 236.33/34.86 Y0, Y1))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 in(Y1, 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 in(Y0, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 in(Y1, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)))) & 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)))) & 236.33/34.86 (setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)) = 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)))) & 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)))) & 236.33/34.86 (setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)) = 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (in(Y1, 236.33/34.86 Y0) => 236.33/34.86 subset( 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset), 236.33/34.86 Y0)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (in(Y1, 236.33/34.86 Y0) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset), 236.33/34.86 powerset( 236.33/34.86 Y0))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset))) => 236.33/34.86 (( 236.33/34.86 Y2 = Y1) | 236.33/34.86 (Y2 = Y0)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 subset( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 subset( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 powerset( 236.33/34.86 powerset( 236.33/34.86 binunion( 236.33/34.86 Y0, Y1)))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y1) => 236.33/34.86 in( 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset)), 236.33/34.86 emptyset)), 236.33/34.86 cartprod( 236.33/34.86 Y0, Y1)))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 cartprod( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y0) & 236.33/34.86 (??(( 236.33/34.86 ^[Y4 : $i]: 236.33/34.86 (in(Y4, 236.33/34.86 Y1) & 236.33/34.86 (Y2 = 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 setadjoin( 236.33/34.86 Y4, 236.33/34.86 emptyset)), 236.33/34.86 emptyset))))))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 cartprod( 236.33/34.86 Y0, Y1)) => 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 setunion( 236.33/34.86 Y2)) & 236.33/34.86 (??(( 236.33/34.86 ^[Y4 : $i]: 236.33/34.86 (in(Y4, 236.33/34.86 setunion( 236.33/34.86 Y2)) & 236.33/34.86 (Y2 = 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset), 236.33/34.86 setadjoin( 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 setadjoin( 236.33/34.86 Y4, 236.33/34.86 emptyset)), 236.33/34.86 emptyset))))))))))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (in(Y1, 236.33/34.86 setunion( 236.33/34.86 Y0)) => 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 in(Y1, 236.33/34.86 Y2)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 subset( 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset)), 236.33/34.86 Y0)))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 subset( 236.33/34.86 Y0, 236.33/34.86 setunion( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset)))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (setunion( 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 emptyset)) = 236.33/34.86 Y0)))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y0) => 236.33/34.86 (Y1(Y2) => 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y2 = Y3))))))))))) => 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2))))) => 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1)) & 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y1) = 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1)) & 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y1) = 236.33/34.86 setadjoin( 236.33/34.86 Y2, 236.33/34.86 emptyset)))))) => 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2)))))))))))) => 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (Y1(Y2) => 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 Y0) => 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y3 = Y2)))))) => 236.33/34.86 (??(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (in(Y3, 236.33/34.86 dsetconstr( 236.33/34.86 Y0, Y1)) & 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y1) = 236.33/34.86 setadjoin( 236.33/34.86 Y3, 236.33/34.86 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.33/34.86 inference('lazy_cnf_imply', [status(thm)], ['182'])). 236.33/34.86 tff('184', plain, 236.33/34.86 ~ ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, dsetconstr(Y0, Y1)) => in(Y2, Y0))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.33/34.86 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.86 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.86 (??(Y0)))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.33/34.86 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.86 (Y0 = Y1))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => 236.33/34.86 (Y0 = emptyset))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y0) => 236.33/34.86 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y0) => 236.33/34.86 (Y1(Y2) => 236.33/34.86 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((??((^[Y1 : $i]: in(Y1, Y0)))) => 236.33/34.86 (Y0 != emptyset))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.33/34.86 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y1) => 236.33/34.86 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.86 (!!((^[Y3 : $o]: 236.33/34.86 (((Y2 = Y0) => Y3) => 236.33/34.86 ((in(Y2, Y1) => Y3) => 236.33/34.86 Y3))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, setadjoin(Y0, Y1)) => 236.33/34.86 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y1) => in(Y2, Y0))))) => 236.33/34.86 in(Y1, powerset(Y0))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y1, powerset(Y0)) => 236.33/34.86 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y1, Y2) => 236.33/34.86 (in(Y2, Y0) => 236.33/34.86 in(Y1, setunion(Y0))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y1, setunion(Y0)) => 236.33/34.86 (!!((^[Y2 : $o]: 236.33/34.86 ((!!((^[Y3 : $i]: 236.33/34.86 (in(Y1, Y3) => 236.33/34.86 (in(Y3, Y0) => 236.33/34.86 Y2))))) => 236.33/34.86 Y2))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y1, Y0) => 236.33/34.86 in(Y1, 236.33/34.86 powerset(setunion(Y0)))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => (Y1 = Y2))))))))) => 236.33/34.86 (??((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ((Y0 != emptyset) => 236.33/34.86 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y0, 236.33/34.86 setadjoin(Y1, emptyset)) => 236.33/34.86 (Y0 = Y1)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((Y0 != Y1) => 236.33/34.86 (~(in(Y1, 236.33/34.86 setadjoin(Y0, 236.33/34.86 emptyset))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 ((Y0 = Y1) => 236.33/34.86 in(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset)) => 236.33/34.86 in(Y1, 236.33/34.86 setadjoin(Y0, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 setadjoin( 236.33/34.86 Y0, 236.33/34.86 setadjoin( 236.33/34.86 Y1, 236.33/34.86 emptyset))) => 236.33/34.86 ((Y2 = Y1) | 236.33/34.86 (Y2 = Y0)))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 in(Y0, 236.33/34.86 setadjoin(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 in(Y1, 236.33/34.86 setadjoin(Y0, 236.33/34.86 setadjoin(Y1, 236.33/34.86 emptyset))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((??((^[Y2 : $i]: 236.33/34.86 (in(Y2, Y0) & 236.33/34.86 Y1(Y2))))) => 236.33/34.86 (dsetconstr(Y0, Y1) != 236.33/34.86 emptyset)))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (in(Y1, emptyset) => 236.33/34.86 Y0(Y1)))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((~((!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (??((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 ( 236.33/34.86 ~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((!!((^[Y2 : $i]: 236.33/34.86 ( 236.33/34.86 in(Y2, 236.33/34.86 Y0) => 236.33/34.86 ( 236.33/34.86 ~( 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (~((??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((~((??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 ( 236.33/34.86 in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (!!((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((??((^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 (~( 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (~((!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $o]: 236.33/34.86 (Y0 => 236.33/34.86 in(emptyset, 236.33/34.86 prop2set(Y0)))))) => 236.33/34.86 ((!!((^[Y0 : $o]: 236.33/34.86 (Y0 => 236.33/34.86 set2prop( 236.33/34.86 prop2set(Y0)))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((~(( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i > $o]: 236.33/34.86 ((~(( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 Y1(Y2))))))) => 236.33/34.86 (??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) & 236.33/34.86 (~( 236.33/34.86 Y1(Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??(Y0)) => 236.33/34.86 ((!!((^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y1) => 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))) => 236.33/34.86 (??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2)))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??((^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) <=> 236.33/34.86 (Y2 = Y1)))))))) => 236.33/34.86 (??((^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y3, 236.33/34.86 Y1)))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!((^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (in(Y2, 236.33/34.86 Y0) <=> 236.33/34.86 in(Y3, 236.33/34.86 Y1)))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 ((??(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 ( 236.33/34.86 Y0(Y1) & 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y1) => 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (Y0(Y2) <=> 236.33/34.86 Y1(Y3))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y0(Y3) => 236.33/34.86 (Y2 = Y3))))))))) <=> 236.33/34.86 ( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y1(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y2 = Y3))))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (setadjoin( 236.33/34.86 Y0, Y2) = 236.33/34.86 setadjoin( 236.33/34.86 Y1, Y3)))))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (powerset( 236.33/34.86 Y0) = 236.33/34.86 powerset( 236.33/34.86 Y1))))))))) => 236.33/34.86 ((!!((^[Y0 : $i]: 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (setunion( 236.33/34.86 Y0) = 236.33/34.86 setunion( 236.33/34.86 Y1))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (Y0(Y1) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y1) => 236.33/34.86 (Y0(Y2) => 236.33/34.86 (Y1 = Y2))))))))))))) => 236.33/34.86 ((!!((^[Y0 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i > $o]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (( 236.33/34.86 Y2 = Y3) => 236.33/34.86 (Y0(Y2) <=> 236.33/34.86 Y1(Y3))))))))) => 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y0(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y0(Y3) => 236.33/34.86 (Y2 = Y3))))))))) => 236.33/34.86 (( 236.33/34.86 ??(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (Y1(Y2) & 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i]: 236.33/34.86 (Y1(Y3) => 236.33/34.86 (Y2 = Y3))))))))) => 236.33/34.86 (descr( 236.33/34.86 Y0) = 236.33/34.86 descr(Y1))))))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i > $o]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y3 : $i > $o]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y4 : $i]: 236.33/34.86 (in(Y4, 236.33/34.86 Y0) => 236.33/34.86 (!!(( 236.33/34.86 ^[Y5 : $i]: 236.33/34.86 (in(Y5, 236.33/34.86 Y1) => 236.33/34.86 (( 236.33/34.86 Y4 = Y5) => 236.33/34.86 (Y2(Y4) <=> 236.33/34.86 Y3(Y5))))))))))) => 236.33/34.86 (dsetconstr( 236.33/34.86 Y0, Y2) = 236.33/34.86 dsetconstr( 236.33/34.86 Y1, Y3)))))))))))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 Y1))))) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 subset( 236.33/34.86 Y1, Y0)))))))) => 236.33/34.86 ((!!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 Y0 = Y1) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (( 236.33/34.86 !!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 Y1))))) => 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!( 236.33/34.86 subset( 236.33/34.86 emptyset))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 in(Y2, 236.33/34.86 Y1)))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (subset( 236.33/34.86 Y0, Y1) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 (~( 236.33/34.86 in(Y2, 236.33/34.86 Y0)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y1 : $i]: 236.33/34.86 (!!(( 236.33/34.86 ^[Y2 : $i]: 236.33/34.86 (in(Y2, 236.33/34.86 Y0) => 236.33/34.86 (( 236.33/34.86 ~( 236.33/34.86 in(Y2, 236.33/34.86 Y1))) => 236.33/34.86 (~( 236.33/34.86 subset( 236.33/34.86 Y0, Y1)))))))))))))) => 236.33/34.86 ( 236.33/34.86 ( 236.33/34.86 !!(( 236.33/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 subset( 236.75/34.86 Y0, Y1))) => 236.75/34.86 (Y0 != Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 (Y0 != Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 subset( 236.75/34.86 Y0, Y0)))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (subset( 236.75/34.86 Y1, Y2) => 236.75/34.86 subset( 236.75/34.86 Y0, Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 Y1, 236.75/34.86 setadjoin( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y2) => 236.75/34.86 subset( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 in(Y0, 236.75/34.86 powerset( 236.75/34.86 Y1))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (subset( 236.75/34.86 Y1, Y0) => 236.75/34.86 (Y0 = Y1))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, 236.75/34.86 emptyset) => 236.75/34.86 (Y0 = 236.75/34.86 emptyset))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y1, Y0) => 236.75/34.86 in(Y1, 236.75/34.86 powerset( 236.75/34.86 Y0))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (in(Y1, 236.75/34.86 powerset( 236.75/34.86 Y0)) => 236.75/34.86 subset( 236.75/34.86 Y1, Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 in(Y0, 236.75/34.86 powerset( 236.75/34.86 Y0))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 subset( 236.75/34.86 powerset( 236.75/34.86 Y0), 236.75/34.86 powerset( 236.75/34.86 Y1))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 in( 236.75/34.86 dsetconstr( 236.75/34.86 Y0, Y1), 236.75/34.86 powerset( 236.75/34.86 Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 subset( 236.75/34.86 dsetconstr( 236.75/34.86 Y0, Y1), 236.75/34.86 Y0))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 in(Y1, 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $o]: 236.75/34.86 (in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (( 236.75/34.86 in(Y2, 236.75/34.86 Y0) => Y3) => 236.75/34.86 (( 236.75/34.86 in(Y2, 236.75/34.86 Y1) => Y3) => 236.75/34.86 Y3))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) | 236.75/34.86 in(Y2, 236.75/34.86 Y0)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 Y0, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 Y1, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 in(Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y2, Y0) => 236.75/34.86 (subset( 236.75/34.86 Y2, Y1) => 236.75/34.86 subset( 236.75/34.86 Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1)) => 236.75/34.86 in(Y2, 236.75/34.86 Y0))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1), 236.75/34.86 Y0))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y1) => 236.75/34.86 subset( 236.75/34.86 Y1, Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1)) => 236.75/34.86 in(Y2, 236.75/34.86 Y1))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 ~(( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 in(Y2, 236.75/34.86 Y1))))))) => 236.75/34.86 (binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 emptyset)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1), 236.75/34.86 Y1))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y1, Y0) => 236.75/34.86 (binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y0) => 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (binintersect( 236.75/34.86 Y0, 236.75/34.86 binunion( 236.75/34.86 Y1, Y2)) = 236.75/34.86 binunion( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1), 236.75/34.86 binintersect( 236.75/34.86 Y0, Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)) => 236.75/34.86 in(Y2, 236.75/34.86 Y0))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (setminus( 236.75/34.86 Y0, Y1) = 236.75/34.86 emptyset)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))) => 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y2, 236.75/34.86 Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 Y0)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y0))) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 setminus( 236.75/34.86 Y0, Y1), 236.75/34.86 Y0))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 setminus( 236.75/34.86 Y0, Y1) = 236.75/34.86 emptyset) => 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $o]: 236.75/34.86 (( 236.75/34.86 in(Y2, 236.75/34.86 Y0) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 Y3)) => 236.75/34.86 (( 236.75/34.86 ( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y0))) => 236.75/34.86 ( 236.75/34.86 in(Y2, 236.75/34.86 Y1) => Y3)) => 236.75/34.86 Y3))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y0))) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y0))) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 in(Y1, 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 in(Y0, 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 in(Y1, 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)))) & 236.75/34.86 (??(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)))) & 236.75/34.86 (setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)) = 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 emptyset))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)))) & 236.75/34.86 (??(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)))) & 236.75/34.86 (setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)) = 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 emptyset))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (in(Y1, 236.75/34.86 Y0) => 236.75/34.86 subset( 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset), 236.75/34.86 Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (in(Y1, 236.75/34.86 Y0) => 236.75/34.86 in( 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset), 236.75/34.86 powerset( 236.75/34.86 Y0))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset), 236.75/34.86 powerset( 236.75/34.86 binunion( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset))) => 236.75/34.86 (( 236.75/34.86 Y2 = Y1) | 236.75/34.86 (Y2 = Y0)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y1) => 236.75/34.86 subset( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y1) => 236.75/34.86 in( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 powerset( 236.75/34.86 binunion( 236.75/34.86 Y0, Y1))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y1) => 236.75/34.86 subset( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)), 236.75/34.86 powerset( 236.75/34.86 binunion( 236.75/34.86 Y0, Y1))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y1) => 236.75/34.86 in( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)), 236.75/34.86 powerset( 236.75/34.86 powerset( 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y1) => 236.75/34.86 in( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)), 236.75/34.86 powerset( 236.75/34.86 powerset( 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y1) => 236.75/34.86 in( 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)), 236.75/34.86 emptyset)), 236.75/34.86 cartprod( 236.75/34.86 Y0, Y1)))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 cartprod( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (??(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y0) & 236.75/34.86 (??(( 236.75/34.86 ^[Y4 : $i]: 236.75/34.86 (in(Y4, 236.75/34.86 Y1) & 236.75/34.86 (Y2 = 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 setadjoin( 236.75/34.86 Y4, 236.75/34.86 emptyset)), 236.75/34.86 emptyset))))))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 cartprod( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (??(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 setunion( 236.75/34.86 Y2)) & 236.75/34.86 (??(( 236.75/34.86 ^[Y4 : $i]: 236.75/34.86 (in(Y4, 236.75/34.86 setunion( 236.75/34.86 Y2)) & 236.75/34.86 (Y2 = 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset), 236.75/34.86 setadjoin( 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 setadjoin( 236.75/34.86 Y4, 236.75/34.86 emptyset)), 236.75/34.86 emptyset))))))))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (in(Y1, 236.75/34.86 setunion( 236.75/34.86 Y0)) => 236.75/34.86 (??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 in(Y1, 236.75/34.86 Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 subset( 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset)), 236.75/34.86 Y0)))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 subset( 236.75/34.86 Y0, 236.75/34.86 setunion( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset)))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (setunion( 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 emptyset)) = 236.75/34.86 Y0)))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 (( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y0) => 236.75/34.86 (Y1(Y2) => 236.75/34.86 (Y1(Y3) => 236.75/34.86 (Y2 = Y3))))))))))) => 236.75/34.86 (( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 Y1(Y2))))) => 236.75/34.86 (??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 dsetconstr( 236.75/34.86 Y0, Y1)) & 236.75/34.86 (dsetconstr( 236.75/34.86 Y0, Y1) = 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 (( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 dsetconstr( 236.75/34.86 Y0, Y1)) & 236.75/34.86 (dsetconstr( 236.75/34.86 Y0, Y1) = 236.75/34.86 setadjoin( 236.75/34.86 Y2, 236.75/34.86 emptyset)))))) => 236.75/34.86 (??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 Y1(Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (Y1(Y2) => 236.75/34.86 (( 236.75/34.86 !!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 Y0) => 236.75/34.86 (Y1(Y3) => 236.75/34.86 (Y3 = Y2)))))) => 236.75/34.86 (??(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (in(Y3, 236.75/34.86 dsetconstr( 236.75/34.86 Y0, Y1)) & 236.75/34.86 (dsetconstr( 236.75/34.86 Y0, Y1) = 236.75/34.86 setadjoin( 236.75/34.86 Y3, 236.75/34.86 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.75/34.86 inference('lazy_cnf_imply', [status(thm)], ['183'])). 236.75/34.86 tff('185', plain, 236.75/34.86 ~ ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 (!!((^[Y2 : $i]: (in(Y2, dsetconstr(Y0, Y1)) => Y1(Y2))))))))))) => 236.75/34.86 ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.86 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 ((??((^[Y1 : $i]: 236.75/34.86 (Y0(Y1) & 236.75/34.86 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.86 (??(Y0)))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.75/34.86 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.86 (Y0 = Y1))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, Y0) => 236.75/34.86 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, Y0) => 236.75/34.86 (Y1(Y2) => 236.75/34.86 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.75/34.86 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, Y1) => 236.75/34.86 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.86 (!!((^[Y3 : $o]: 236.75/34.86 (((Y2 = Y0) => Y3) => 236.75/34.86 ((in(Y2, Y1) => Y3) => 236.75/34.86 Y3))))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.86 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 ((!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.86 in(Y1, powerset(Y0))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.86 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y1, powerset(Y0)) => 236.75/34.86 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y1, Y2) => 236.75/34.86 (in(Y2, Y0) => 236.75/34.86 in(Y1, setunion(Y0))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (in(Y1, setunion(Y0)) => 236.75/34.86 (!!((^[Y2 : $o]: 236.75/34.86 ((!!((^[Y3 : $i]: 236.75/34.86 (in(Y1, Y3) => 236.75/34.86 (in(Y3, Y0) => 236.75/34.86 Y2))))) => 236.75/34.86 Y2))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (in(Y1, Y0) => 236.75/34.86 in(Y1, powerset(setunion(Y0)))))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 ((??((^[Y1 : $i]: 236.75/34.86 (Y0(Y1) & 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.86 (??((^[Y1 : $i]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 ((Y0 != emptyset) => 236.75/34.86 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (in(Y0, 236.75/34.86 setadjoin(Y1, emptyset)) => 236.75/34.86 (Y0 = Y1)))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 ((Y0 != Y1) => 236.75/34.86 (~(in(Y1, 236.75/34.86 setadjoin(Y0, 236.75/34.86 emptyset))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 ((Y0 = Y1) => 236.75/34.86 in(Y0, 236.75/34.86 setadjoin(Y1, emptyset))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (in(Y0, 236.75/34.86 setadjoin(Y1, 236.75/34.86 emptyset)) => 236.75/34.86 in(Y1, 236.75/34.86 setadjoin(Y0, 236.75/34.86 emptyset))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setadjoin(Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset))) => 236.75/34.86 ((Y2 = Y1) | 236.75/34.86 (Y2 = Y0)))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 in(Y0, 236.75/34.86 setadjoin(Y0, 236.75/34.86 setadjoin(Y1, 236.75/34.86 emptyset))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 in(Y1, 236.75/34.86 setadjoin(Y0, 236.75/34.86 setadjoin(Y1, 236.75/34.86 emptyset))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 ((??((^[Y2 : $i]: 236.75/34.86 (in(Y2, Y0) & 236.75/34.86 Y1(Y2))))) => 236.75/34.86 (dsetconstr(Y0, Y1) != 236.75/34.86 emptyset)))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (in(Y1, emptyset) => 236.75/34.86 Y0(Y1)))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 ((~((!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 Y1(Y2))))))) => 236.75/34.86 (??((^[Y2 : $i]: 236.75/34.86 (in(Y2, Y0) & 236.75/34.86 (~(Y1(Y2)))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 ((!!((^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 ( 236.75/34.86 ~( 236.75/34.86 Y1(Y2))))))) => 236.75/34.86 (~((??((^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 Y1(Y2)))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 ((~((??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 Y1(Y2))))))) => 236.75/34.86 (!!((^[Y2 : $i]: 236.75/34.86 ( 236.75/34.86 in(Y2, 236.75/34.86 Y0) => 236.75/34.86 ( 236.75/34.86 ~( 236.75/34.86 Y1(Y2)))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 ((??((^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 (~( 236.75/34.86 Y1(Y2))))))) => 236.75/34.86 (~((!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 ( 236.75/34.86 in(Y2, 236.75/34.86 Y0) => 236.75/34.86 Y1(Y2)))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $o]: 236.75/34.86 (Y0 => 236.75/34.86 in(emptyset, 236.75/34.86 prop2set(Y0)))))) => 236.75/34.86 ((!!((^[Y0 : $o]: 236.75/34.86 (Y0 => 236.75/34.86 set2prop( 236.75/34.86 prop2set(Y0)))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 ((~(( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 ( 236.75/34.86 in(Y2, 236.75/34.86 Y0) & 236.75/34.86 Y1(Y2))))))) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 ( 236.75/34.86 in(Y2, 236.75/34.86 Y0) => 236.75/34.86 ( 236.75/34.86 ~( 236.75/34.86 Y1(Y2)))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i > $o]: 236.75/34.86 ((~(( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 Y1(Y2))))))) => 236.75/34.86 (??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 (~( 236.75/34.86 Y1(Y2)))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 ((??(Y0)) => 236.75/34.86 ((!!((^[Y1 : $i]: 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y1) => 236.75/34.86 (Y0(Y2) => 236.75/34.86 (Y1 = Y2))))))))) => 236.75/34.86 (??((^[Y1 : $i]: 236.75/34.86 ( 236.75/34.86 Y0(Y1) & 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y2) => 236.75/34.86 (Y1 = Y2)))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 ((??((^[Y1 : $i]: 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y2) <=> 236.75/34.86 (Y2 = Y1)))))))) => 236.75/34.86 (??((^[Y1 : $i]: 236.75/34.86 ( 236.75/34.86 Y0(Y1) & 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y2) => 236.75/34.86 (Y1 = Y2))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 Y0 = Y1) => 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (( 236.75/34.86 Y2 = Y3) => 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y3, 236.75/34.86 Y1)))))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!((^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 Y0 = Y1) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (( 236.75/34.86 Y2 = Y3) => 236.75/34.86 (in(Y2, 236.75/34.86 Y0) <=> 236.75/34.86 in(Y3, 236.75/34.86 Y1)))))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 ((??(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (Y0(Y1) & 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y2) => 236.75/34.86 (Y1 = Y2))))))))) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y1) => 236.75/34.86 (Y0(Y2) => 236.75/34.86 (Y1 = Y2))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 (( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (( 236.75/34.86 Y2 = Y3) => 236.75/34.86 (Y0(Y2) <=> 236.75/34.86 Y1(Y3))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y2) & 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (Y0(Y3) => 236.75/34.86 (Y2 = Y3))))))))) <=> 236.75/34.86 ( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y1(Y2) & 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (Y1(Y3) => 236.75/34.86 (Y2 = Y3))))))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 Y0 = Y1) => 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (( 236.75/34.86 Y2 = Y3) => 236.75/34.86 (setadjoin( 236.75/34.86 Y0, Y2) = 236.75/34.86 setadjoin( 236.75/34.86 Y1, Y3)))))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 Y0 = Y1) => 236.75/34.86 (powerset( 236.75/34.86 Y0) = 236.75/34.86 powerset( 236.75/34.86 Y1))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 Y0 = Y1) => 236.75/34.86 (setunion( 236.75/34.86 Y0) = 236.75/34.86 setunion( 236.75/34.86 Y1))))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 ??(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (Y0(Y1) & 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y2) => 236.75/34.86 (Y1 = Y2))))))))) => 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y1) => 236.75/34.86 (Y0(Y2) => 236.75/34.86 (Y1 = Y2))))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i > $o]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 (( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (( 236.75/34.86 Y2 = Y3) => 236.75/34.86 (Y0(Y2) <=> 236.75/34.86 Y1(Y3))))))))) => 236.75/34.86 (( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y0(Y2) & 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (Y0(Y3) => 236.75/34.86 (Y2 = Y3))))))))) => 236.75/34.86 (( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (Y1(Y2) & 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i]: 236.75/34.86 (Y1(Y3) => 236.75/34.86 (Y2 = Y3))))))))) => 236.75/34.86 (descr( 236.75/34.86 Y0) = 236.75/34.86 descr(Y1))))))))))) => 236.75/34.86 ((!!((^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 Y0 = Y1) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i > $o]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $i > $o]: 236.75/34.86 (( 236.75/34.86 !!(( 236.75/34.86 ^[Y4 : $i]: 236.75/34.86 (in(Y4, 236.75/34.86 Y0) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y5 : $i]: 236.75/34.86 (in(Y5, 236.75/34.86 Y1) => 236.75/34.86 (( 236.75/34.86 Y4 = Y5) => 236.75/34.86 (Y2(Y4) <=> 236.75/34.86 Y3(Y5))))))))))) => 236.75/34.86 (dsetconstr( 236.75/34.86 Y0, Y2) = 236.75/34.86 dsetconstr( 236.75/34.86 Y1, Y3)))))))))))))))) => 236.75/34.86 ((!!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y2, 236.75/34.86 Y1))))) => 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ((!!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 Y0 = Y1) => 236.75/34.86 subset( 236.75/34.86 Y1, Y0)))))))) => 236.75/34.86 ((!!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 Y0 = Y1) => 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ((!!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 !!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y2, 236.75/34.86 Y1))))) => 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 (( 236.75/34.86 !!( 236.75/34.86 subset( 236.75/34.86 emptyset))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y2, 236.75/34.86 Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 Y0)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 (~( 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 subset( 236.75/34.86 Y0, Y1))) => 236.75/34.86 (Y0 != Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 (Y0 != Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 subset( 236.75/34.86 Y0, Y0)))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (subset( 236.75/34.86 Y1, Y2) => 236.75/34.86 subset( 236.75/34.86 Y0, Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 Y1, 236.75/34.86 setadjoin( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y2) => 236.75/34.86 subset( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 in(Y0, 236.75/34.86 powerset( 236.75/34.86 Y1))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (subset( 236.75/34.86 Y1, Y0) => 236.75/34.86 (Y0 = Y1))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, 236.75/34.86 emptyset) => 236.75/34.86 (Y0 = 236.75/34.86 emptyset))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y1, Y0) => 236.75/34.86 in(Y1, 236.75/34.86 powerset( 236.75/34.86 Y0))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (in(Y1, 236.75/34.86 powerset( 236.75/34.86 Y0)) => 236.75/34.86 subset( 236.75/34.86 Y1, Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 in(Y0, 236.75/34.86 powerset( 236.75/34.86 Y0))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 subset( 236.75/34.86 powerset( 236.75/34.86 Y0), 236.75/34.86 powerset( 236.75/34.86 Y1))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 in( 236.75/34.86 dsetconstr( 236.75/34.86 Y0, Y1), 236.75/34.86 powerset( 236.75/34.86 Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i > $o]: 236.75/34.86 subset( 236.75/34.86 dsetconstr( 236.75/34.86 Y0, Y1), 236.75/34.86 Y0))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 in(Y1, 236.75/34.86 setadjoin( 236.75/34.86 Y0, 236.75/34.86 setadjoin( 236.75/34.86 Y1, 236.75/34.86 emptyset))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $o]: 236.75/34.86 (in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (( 236.75/34.86 in(Y2, 236.75/34.86 Y0) => Y3) => 236.75/34.86 (( 236.75/34.86 in(Y2, 236.75/34.86 Y1) => Y3) => 236.75/34.86 Y3))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) | 236.75/34.86 in(Y2, 236.75/34.86 Y0)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 Y0, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 Y1, 236.75/34.86 binunion( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 in(Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y2, Y0) => 236.75/34.86 (subset( 236.75/34.86 Y2, Y1) => 236.75/34.86 subset( 236.75/34.86 Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1)) => 236.75/34.86 in(Y2, 236.75/34.86 Y0))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1), 236.75/34.86 Y0))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y1) => 236.75/34.86 subset( 236.75/34.86 Y1, Y0)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1)) => 236.75/34.86 in(Y2, 236.75/34.86 Y1))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 ~(( 236.75/34.86 ??(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) & 236.75/34.86 in(Y2, 236.75/34.86 Y1))))))) => 236.75/34.86 (binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 emptyset)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1), 236.75/34.86 Y1))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y1, Y0) => 236.75/34.86 (binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1) = 236.75/34.86 Y0) => 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (binintersect( 236.75/34.86 Y0, 236.75/34.86 binunion( 236.75/34.86 Y1, Y2)) = 236.75/34.86 binunion( 236.75/34.86 binintersect( 236.75/34.86 Y0, Y1), 236.75/34.86 binintersect( 236.75/34.86 Y0, Y2)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)) => 236.75/34.86 in(Y2, 236.75/34.86 Y0))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (subset( 236.75/34.86 Y0, Y1) => 236.75/34.86 (setminus( 236.75/34.86 Y0, Y1) = 236.75/34.86 emptyset)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))) => 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 in(Y2, 236.75/34.86 Y1)))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 Y0)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y0))) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.86 setminus( 236.75/34.86 Y0, Y1)))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 subset( 236.75/34.86 setminus( 236.75/34.86 Y0, Y1), 236.75/34.86 Y0))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (( 236.75/34.86 setminus( 236.75/34.86 Y0, Y1) = 236.75/34.86 emptyset) => 236.75/34.86 subset( 236.75/34.86 Y0, Y1)))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1)) => 236.75/34.86 (!!(( 236.75/34.86 ^[Y3 : $o]: 236.75/34.86 (( 236.75/34.86 in(Y2, 236.75/34.86 Y0) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 Y3)) => 236.75/34.86 (( 236.75/34.86 ( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y0))) => 236.75/34.86 ( 236.75/34.86 in(Y2, 236.75/34.86 Y1) => Y3)) => 236.75/34.86 Y3))))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y1))) => 236.75/34.86 in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (( 236.75/34.86 ~( 236.75/34.86 in(Y2, 236.75/34.86 Y0))) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 in(Y2, 236.75/34.86 symdiff( 236.75/34.86 Y0, Y1))))))))))))) => 236.75/34.86 ( 236.75/34.86 ( 236.75/34.86 !!(( 236.75/34.86 ^[Y0 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y1 : $i]: 236.75/34.86 (!!(( 236.75/34.86 ^[Y2 : $i]: 236.75/34.86 (in(Y2, 236.75/34.86 Y0) => 236.75/34.86 (in(Y2, 236.75/34.86 Y1) => 236.75/34.86 (~( 236.75/34.86 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)) = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)) = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 Y0) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset), 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 Y0) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset), 236.75/34.87 powerset( 236.75/34.87 Y0))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))) => 236.75/34.87 (( 236.75/34.87 Y2 = Y1) | 236.75/34.87 (Y2 = Y0)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) & 236.75/34.87 (??(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 Y1) & 236.75/34.87 (Y2 = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 setadjoin( 236.75/34.87 Y4, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 Y2)) & 236.75/34.87 (??(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 setunion( 236.75/34.87 Y2)) & 236.75/34.87 (Y2 = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 setadjoin( 236.75/34.87 Y4, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 setunion( 236.75/34.87 Y0)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 in(Y1, 236.75/34.87 Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)), 236.75/34.87 Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)) = 236.75/34.87 Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset)))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y3 = Y2)))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.75/34.87 inference('lazy_cnf_imply', [status(thm)], ['184'])). 236.75/34.87 tff('186', plain, 236.75/34.87 ~ ((!!((^[Y0 : $o]: (!!((^[Y1 : $i]: (in(Y1, prop2set(Y0)) => Y0))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.87 (??(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.75/34.87 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.87 (Y0 = Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.75/34.87 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y1) => 236.75/34.87 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.87 (!!((^[Y3 : $o]: 236.75/34.87 (((Y2 = Y0) => Y3) => 236.75/34.87 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.87 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.87 in(Y1, powerset(Y0))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y1, powerset(Y0)) => 236.75/34.87 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y1, Y2) => 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 in(Y1, setunion(Y0))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, setunion(Y0)) => 236.75/34.87 (!!((^[Y2 : $o]: 236.75/34.87 ((!!((^[Y3 : $i]: 236.75/34.87 (in(Y1, Y3) => 236.75/34.87 (in(Y3, Y0) => 236.75/34.87 Y2))))) => 236.75/34.87 Y2))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, Y0) => 236.75/34.87 in(Y1, powerset(setunion(Y0)))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((Y0 != emptyset) => 236.75/34.87 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y0, 236.75/34.87 setadjoin(Y1, emptyset)) => 236.75/34.87 (Y0 = Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 != Y1) => 236.75/34.87 (~(in(Y1, 236.75/34.87 setadjoin(Y0, 236.75/34.87 emptyset))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 = Y1) => 236.75/34.87 in(Y0, 236.75/34.87 setadjoin(Y1, emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y0, 236.75/34.87 setadjoin(Y1, emptyset)) => 236.75/34.87 in(Y1, 236.75/34.87 setadjoin(Y0, emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))) => 236.75/34.87 ((Y2 = Y1) | 236.75/34.87 (Y2 = Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) & 236.75/34.87 Y1(Y2))))) => 236.75/34.87 (dsetconstr(Y0, Y1) != 236.75/34.87 emptyset)))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, emptyset) => 236.75/34.87 Y0(Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((!!((^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (??((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) & 236.75/34.87 (~(Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (~(Y1(Y2))))))) => 236.75/34.87 (~((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((??((^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y0) & 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (~((!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $o]: 236.75/34.87 (Y0 => 236.75/34.87 in(emptyset, 236.75/34.87 prop2set(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $o]: 236.75/34.87 (Y0 => 236.75/34.87 set2prop( 236.75/34.87 prop2set(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~(( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y0) & 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??(Y0)) => 236.75/34.87 ((!!((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 (Y2 = Y1)))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y3, 236.75/34.87 Y1)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) <=> 236.75/34.87 in(Y3, 236.75/34.87 Y1)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 Y1(Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y0(Y3) => 236.75/34.87 (Y2 = Y3))))))))) <=> 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y1(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (setadjoin( 236.75/34.87 Y0, Y2) = 236.75/34.87 setadjoin( 236.75/34.87 Y1, Y3)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 powerset( 236.75/34.87 Y0) = 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 (setunion( 236.75/34.87 Y0) = 236.75/34.87 setunion( 236.75/34.87 Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 Y1(Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y0(Y3) => 236.75/34.87 (Y2 = Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y1(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))) => 236.75/34.87 (descr( 236.75/34.87 Y0) = 236.75/34.87 descr(Y1))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y5 : $i]: 236.75/34.87 (in(Y5, 236.75/34.87 Y1) => 236.75/34.87 (( 236.75/34.87 Y4 = Y5) => 236.75/34.87 (Y2(Y4) <=> 236.75/34.87 Y3(Y5))))))))))) => 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y2) = 236.75/34.87 dsetconstr( 236.75/34.87 Y1, Y3)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!( 236.75/34.87 subset( 236.75/34.87 emptyset))) => 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 subset( 236.75/34.87 Y0, Y1))) => 236.75/34.87 (Y0 != Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (Y0 != Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (subset( 236.75/34.87 Y1, Y2) => 236.75/34.87 subset( 236.75/34.87 Y0, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y2) => 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 in(Y0, 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 (Y0 = Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, 236.75/34.87 emptyset) => 236.75/34.87 (Y0 = 236.75/34.87 emptyset))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 in(Y1, 236.75/34.87 powerset( 236.75/34.87 Y0))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 powerset( 236.75/34.87 Y0)) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 powerset( 236.75/34.87 Y0))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 subset( 236.75/34.87 powerset( 236.75/34.87 Y0), 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 in( 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1), 236.75/34.87 powerset( 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 subset( 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $o]: 236.75/34.87 (in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y0) => Y3) => 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y1) => Y3) => 236.75/34.87 Y3))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) | 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y1, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y2, Y0) => 236.75/34.87 (subset( 236.75/34.87 Y2, Y1) => 236.75/34.87 subset( 236.75/34.87 Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y0))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 ~(( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 emptyset)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 Y1))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y0) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (binintersect( 236.75/34.87 Y0, 236.75/34.87 binunion( 236.75/34.87 Y1, Y2)) = 236.75/34.87 binunion( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 binintersect( 236.75/34.87 Y0, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y0))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (setminus( 236.75/34.87 Y0, Y1) = 236.75/34.87 emptyset)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 setminus( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 setminus( 236.75/34.87 Y0, Y1) = 236.75/34.87 emptyset) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $o]: 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y0) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 Y3)) => 236.75/34.87 (( 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y1) => Y3)) => 236.75/34.87 Y3))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)) = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)) = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 Y0) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset), 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 Y0) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset), 236.75/34.87 powerset( 236.75/34.87 Y0))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))) => 236.75/34.87 (( 236.75/34.87 Y2 = Y1) | 236.75/34.87 (Y2 = Y0)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) & 236.75/34.87 (??(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 Y1) & 236.75/34.87 (Y2 = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 setadjoin( 236.75/34.87 Y4, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 Y2)) & 236.75/34.87 (??(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 setunion( 236.75/34.87 Y2)) & 236.75/34.87 (Y2 = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 setadjoin( 236.75/34.87 Y4, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 setunion( 236.75/34.87 Y0)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 in(Y1, 236.75/34.87 Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)), 236.75/34.87 Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)) = 236.75/34.87 Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset)))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y3 = Y2)))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.75/34.87 inference('lazy_cnf_imply', [status(thm)], ['185'])). 236.75/34.87 tff('187', plain, 236.75/34.87 ~ ((!!((^[Y0 : $i]: (in(Y0, emptyset) => (!!((^[Y1 : $o]: Y1))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.87 (??(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.75/34.87 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.87 (Y0 = Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.75/34.87 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y1) => 236.75/34.87 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.87 (!!((^[Y3 : $o]: 236.75/34.87 (((Y2 = Y0) => Y3) => 236.75/34.87 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.87 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.87 in(Y1, powerset(Y0))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y1, powerset(Y0)) => 236.75/34.87 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y1, Y2) => 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 in(Y1, setunion(Y0))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, setunion(Y0)) => 236.75/34.87 (!!((^[Y2 : $o]: 236.75/34.87 ((!!((^[Y3 : $i]: 236.75/34.87 (in(Y1, Y3) => 236.75/34.87 (in(Y3, Y0) => Y2))))) => 236.75/34.87 Y2))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, Y0) => 236.75/34.87 in(Y1, powerset(setunion(Y0)))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((Y0 != emptyset) => 236.75/34.87 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y0, 236.75/34.87 setadjoin(Y1, emptyset)) => 236.75/34.87 (Y0 = Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 != Y1) => 236.75/34.87 (~(in(Y1, 236.75/34.87 setadjoin(Y0, emptyset))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 = Y1) => 236.75/34.87 in(Y0, 236.75/34.87 setadjoin(Y1, emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y0, 236.75/34.87 setadjoin(Y1, emptyset)) => 236.75/34.87 in(Y1, 236.75/34.87 setadjoin(Y0, emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))) => 236.75/34.87 ((Y2 = Y1) | 236.75/34.87 (Y2 = Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) & 236.75/34.87 Y1(Y2))))) => 236.75/34.87 (dsetconstr(Y0, Y1) != 236.75/34.87 emptyset)))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, emptyset) => 236.75/34.87 Y0(Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (??((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) & 236.75/34.87 (~(Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (~(Y1(Y2))))))) => 236.75/34.87 (~((??((^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (~(Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (~((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $o]: 236.75/34.87 (Y0 => 236.75/34.87 in(emptyset, 236.75/34.87 prop2set(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $o]: 236.75/34.87 (Y0 => 236.75/34.87 set2prop(prop2set(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (~( 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??(Y0)) => 236.75/34.87 ((!!((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 (Y2 = Y1)))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y3, 236.75/34.87 Y1)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) <=> 236.75/34.87 in(Y3, 236.75/34.87 Y1)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 Y1(Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y0(Y3) => 236.75/34.87 (Y2 = Y3))))))))) <=> 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y1(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (setadjoin( 236.75/34.87 Y0, Y2) = 236.75/34.87 setadjoin( 236.75/34.87 Y1, Y3)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 powerset( 236.75/34.87 Y0) = 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 setunion( 236.75/34.87 Y0) = 236.75/34.87 setunion( 236.75/34.87 Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 Y1(Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y0(Y3) => 236.75/34.87 (Y2 = Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y1(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))) => 236.75/34.87 (descr( 236.75/34.87 Y0) = 236.75/34.87 descr(Y1))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y5 : $i]: 236.75/34.87 (in(Y5, 236.75/34.87 Y1) => 236.75/34.87 (( 236.75/34.87 Y4 = Y5) => 236.75/34.87 (Y2(Y4) <=> 236.75/34.87 Y3(Y5))))))))))) => 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y2) = 236.75/34.87 dsetconstr( 236.75/34.87 Y1, Y3)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!( 236.75/34.87 subset( 236.75/34.87 emptyset))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1)))))))))))) => 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 subset( 236.75/34.87 Y0, Y1))) => 236.75/34.87 (Y0 != Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (Y0 != Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (subset( 236.75/34.87 Y1, Y2) => 236.75/34.87 subset( 236.75/34.87 Y0, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y2) => 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 in(Y0, 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 (Y0 = Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, 236.75/34.87 emptyset) => 236.75/34.87 (Y0 = 236.75/34.87 emptyset))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 in(Y1, 236.75/34.87 powerset( 236.75/34.87 Y0))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 powerset( 236.75/34.87 Y0)) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 powerset( 236.75/34.87 Y0))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 subset( 236.75/34.87 powerset( 236.75/34.87 Y0), 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 in( 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1), 236.75/34.87 powerset( 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 subset( 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $o]: 236.75/34.87 (in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y0) => Y3) => 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y1) => Y3) => 236.75/34.87 Y3))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) | 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y1, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y2, Y0) => 236.75/34.87 (subset( 236.75/34.87 Y2, Y1) => 236.75/34.87 subset( 236.75/34.87 Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y0))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 ~(( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 emptyset)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 Y1))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y0) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (binintersect( 236.75/34.87 Y0, 236.75/34.87 binunion( 236.75/34.87 Y1, Y2)) = 236.75/34.87 binunion( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 binintersect( 236.75/34.87 Y0, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y0))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (setminus( 236.75/34.87 Y0, Y1) = 236.75/34.87 emptyset)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 setminus( 236.75/34.87 Y0, Y1)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 setminus( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 setminus( 236.75/34.87 Y0, Y1) = 236.75/34.87 emptyset) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $o]: 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y0) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 Y3)) => 236.75/34.87 (( 236.75/34.87 ( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y1) => Y3)) => 236.75/34.87 Y3))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y0))) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 symdiff( 236.75/34.87 Y0, Y1))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)) = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)))) & 236.75/34.87 (setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)) = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 Y0) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset), 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 Y0) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset), 236.75/34.87 powerset( 236.75/34.87 Y0))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))) => 236.75/34.87 (( 236.75/34.87 Y2 = Y1) | 236.75/34.87 (Y2 = Y0)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 powerset( 236.75/34.87 powerset( 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y1) => 236.75/34.87 in( 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset)), 236.75/34.87 emptyset)), 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) & 236.75/34.87 (??(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 Y1) & 236.75/34.87 (Y2 = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 setadjoin( 236.75/34.87 Y4, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 cartprod( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 setunion( 236.75/34.87 Y2)) & 236.75/34.87 (??(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 setunion( 236.75/34.87 Y2)) & 236.75/34.87 (Y2 = 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset), 236.75/34.87 setadjoin( 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 setadjoin( 236.75/34.87 Y4, 236.75/34.87 emptyset)), 236.75/34.87 emptyset))))))))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 setunion( 236.75/34.87 Y0)) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 in(Y1, 236.75/34.87 Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)), 236.75/34.87 Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (setunion( 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 emptyset)) = 236.75/34.87 Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y2, 236.75/34.87 emptyset)))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 Y0) => 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y3 = Y2)))))) => 236.75/34.87 (??(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (in(Y3, 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1)) & 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y1) = 236.75/34.87 setadjoin( 236.75/34.87 Y3, 236.75/34.87 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.75/34.87 inference('lazy_cnf_imply', [status(thm)], ['186'])). 236.75/34.87 tff('188', plain, 236.75/34.87 ~ ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.87 (??(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.75/34.87 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.87 (Y0 = Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (Y1(Y2) => 236.75/34.87 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.75/34.87 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y1) => 236.75/34.87 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.87 (!!((^[Y3 : $o]: 236.75/34.87 (((Y2 = Y0) => Y3) => 236.75/34.87 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.87 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.87 in(Y1, powerset(Y0))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.87 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y1, powerset(Y0)) => 236.75/34.87 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y1, Y2) => 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 in(Y1, setunion(Y0))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, setunion(Y0)) => 236.75/34.87 (!!((^[Y2 : $o]: 236.75/34.87 ((!!((^[Y3 : $i]: 236.75/34.87 (in(Y1, Y3) => 236.75/34.87 (in(Y3, Y0) => Y2))))) => 236.75/34.87 Y2))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, Y0) => 236.75/34.87 in(Y1, powerset(setunion(Y0)))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ((Y0 != emptyset) => 236.75/34.87 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y0, 236.75/34.87 setadjoin(Y1, emptyset)) => 236.75/34.87 (Y0 = Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 != Y1) => 236.75/34.87 (~(in(Y1, 236.75/34.87 setadjoin(Y0, emptyset))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 = Y1) => 236.75/34.87 in(Y0, 236.75/34.87 setadjoin(Y1, emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y0, 236.75/34.87 setadjoin(Y1, emptyset)) => 236.75/34.87 in(Y1, 236.75/34.87 setadjoin(Y0, emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))) => 236.75/34.87 ((Y2 = Y1) | 236.75/34.87 (Y2 = Y0)))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin(Y0, 236.75/34.87 setadjoin(Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) & 236.75/34.87 Y1(Y2))))) => 236.75/34.87 (dsetconstr(Y0, Y1) != 236.75/34.87 emptyset)))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (in(Y1, emptyset) => 236.75/34.87 Y0(Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (??((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) & 236.75/34.87 (~(Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (~(Y1(Y2))))))) => 236.75/34.87 (~((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((??((^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) => 236.75/34.87 (~(Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((??((^[Y2 : $i]: 236.75/34.87 (in(Y2, Y0) & 236.75/34.87 (~(Y1(Y2))))))) => 236.75/34.87 (~((!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $o]: 236.75/34.87 (Y0 => 236.75/34.87 in(emptyset, 236.75/34.87 prop2set(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $o]: 236.75/34.87 (Y0 => 236.75/34.87 set2prop(prop2set(Y0)))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 in(Y2, 236.75/34.87 Y0) & 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (!!((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (~( 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ((~((!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 Y1(Y2))))))) => 236.75/34.87 (??((^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 (~( 236.75/34.87 Y1(Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??(Y0)) => 236.75/34.87 ((!!((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 Y0(Y1) => 236.75/34.87 ( 236.75/34.87 Y0(Y2) => 236.75/34.87 ( 236.75/34.87 Y1 = Y2))))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2)))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 ( 236.75/34.87 Y0(Y2) <=> 236.75/34.87 ( 236.75/34.87 Y2 = Y1)))))))) => 236.75/34.87 (??((^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y3, 236.75/34.87 Y1)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ((Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) <=> 236.75/34.87 in(Y3, 236.75/34.87 Y1)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??((^[Y1 : $i]: 236.75/34.87 ( 236.75/34.87 Y0(Y1) & 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!((^[Y1 : $i > $o]: 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 Y1(Y3))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y0(Y3) => 236.75/34.87 (Y2 = Y3))))))))) <=> 236.75/34.87 ( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y1(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (setadjoin( 236.75/34.87 Y0, Y2) = 236.75/34.87 setadjoin( 236.75/34.87 Y1, Y3)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!((^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 (powerset( 236.75/34.87 Y0) = 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 ( 236.75/34.87 setunion( 236.75/34.87 Y0) = 236.75/34.87 setunion( 236.75/34.87 Y1))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 ((??(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (Y0(Y1) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y1) => 236.75/34.87 (Y0(Y2) => 236.75/34.87 (Y1 = Y2))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (( 236.75/34.87 Y2 = Y3) => 236.75/34.87 (Y0(Y2) <=> 236.75/34.87 Y1(Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y0(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y0(Y3) => 236.75/34.87 (Y2 = Y3))))))))) => 236.75/34.87 (( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (Y1(Y2) & 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i]: 236.75/34.87 (Y1(Y3) => 236.75/34.87 (Y2 = Y3))))))))) => 236.75/34.87 (descr( 236.75/34.87 Y0) = 236.75/34.87 descr(Y1))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i > $o]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $i > $o]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y4 : $i]: 236.75/34.87 (in(Y4, 236.75/34.87 Y0) => 236.75/34.87 (!!(( 236.75/34.87 ^[Y5 : $i]: 236.75/34.87 (in(Y5, 236.75/34.87 Y1) => 236.75/34.87 (( 236.75/34.87 Y4 = Y5) => 236.75/34.87 (Y2(Y4) <=> 236.75/34.87 Y3(Y5))))))))))) => 236.75/34.87 (dsetconstr( 236.75/34.87 Y0, Y2) = 236.75/34.87 dsetconstr( 236.75/34.87 Y1, Y3)))))))))))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ((!!((^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 Y0 = Y1) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ((!!( 236.75/34.87 subset( 236.75/34.87 emptyset))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 Y1)))))))))))) => 236.75/34.87 ((!!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))))) => 236.75/34.87 (( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (~( 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 subset( 236.75/34.87 Y0, Y1))) => 236.75/34.87 (Y0 != Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 (Y0 != Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, Y0)))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (subset( 236.75/34.87 Y1, Y2) => 236.75/34.87 subset( 236.75/34.87 Y0, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y2) => 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 in(Y0, 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 (Y0 = Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, 236.75/34.87 emptyset) => 236.75/34.87 (Y0 = 236.75/34.87 emptyset))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 in(Y1, 236.75/34.87 powerset( 236.75/34.87 Y0))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (in(Y1, 236.75/34.87 powerset( 236.75/34.87 Y0)) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 in(Y0, 236.75/34.87 powerset( 236.75/34.87 Y0))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 subset( 236.75/34.87 powerset( 236.75/34.87 Y0), 236.75/34.87 powerset( 236.75/34.87 Y1))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 in( 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1), 236.75/34.87 powerset( 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i > $o]: 236.75/34.87 subset( 236.75/34.87 dsetconstr( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 in(Y1, 236.75/34.87 setadjoin( 236.75/34.87 Y0, 236.75/34.87 setadjoin( 236.75/34.87 Y1, 236.75/34.87 emptyset))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y3 : $o]: 236.75/34.87 (in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y0) => Y3) => 236.75/34.87 (( 236.75/34.87 in(Y2, 236.75/34.87 Y1) => Y3) => 236.75/34.87 Y3))))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) | 236.75/34.87 in(Y2, 236.75/34.87 Y0)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y0, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 Y1, 236.75/34.87 binunion( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (in(Y2, 236.75/34.87 Y1) => 236.75/34.87 in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y2, Y0) => 236.75/34.87 (subset( 236.75/34.87 Y2, Y1) => 236.75/34.87 subset( 236.75/34.87 Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1))))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y0))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 Y0))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y0, Y1) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y1) => 236.75/34.87 subset( 236.75/34.87 Y1, Y0)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1)) => 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 ~(( 236.75/34.87 ??(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) & 236.75/34.87 in(Y2, 236.75/34.87 Y1))))))) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 emptyset)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 subset( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 Y1))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (subset( 236.75/34.87 Y1, Y0) => 236.75/34.87 (binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1) = 236.75/34.87 Y0) => 236.75/34.87 subset( 236.75/34.87 Y0, Y1)))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (binintersect( 236.75/34.87 Y0, 236.75/34.87 binunion( 236.75/34.87 Y1, Y2)) = 236.75/34.87 binunion( 236.75/34.87 binintersect( 236.75/34.87 Y0, Y1), 236.75/34.87 binintersect( 236.75/34.87 Y0, Y2)))))))))))) => 236.75/34.87 ( 236.75/34.87 ( 236.75/34.87 !!(( 236.75/34.87 ^[Y0 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y1 : $i]: 236.75/34.87 (!!(( 236.75/34.87 ^[Y2 : $i]: 236.75/34.87 (in(Y2, 236.75/34.87 Y0) => 236.75/34.87 (( 236.75/34.87 ~( 236.75/34.87 in(Y2, 236.75/34.87 Y1))) => 236.75/34.87 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)) => 236.75/34.88 in(Y2, 236.75/34.88 Y0))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 (setminus( 236.75/34.88 Y0, Y1) = 236.75/34.88 emptyset)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))) => 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in(Y2, 236.75/34.88 Y1)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 Y0)))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 subset( 236.75/34.88 setminus( 236.75/34.88 Y0, Y1), 236.75/34.88 Y0))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 setminus( 236.75/34.88 Y0, Y1) = 236.75/34.88 emptyset) => 236.75/34.88 subset( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $o]: 236.75/34.88 (( 236.75/34.88 in(Y2, 236.75/34.88 Y0) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 Y3)) => 236.75/34.88 (( 236.75/34.88 ( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 ( 236.75/34.88 in(Y2, 236.75/34.88 Y1) => Y3)) => 236.75/34.88 Y3))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 in(Y1, 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 in(Y0, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 in(Y1, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (??(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)) = 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (??(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)) = 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (in(Y1, 236.75/34.88 Y0) => 236.75/34.88 subset( 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset), 236.75/34.88 Y0)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (in(Y1, 236.75/34.88 Y0) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset), 236.75/34.88 powerset( 236.75/34.88 Y0))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 powerset( 236.75/34.88 binunion( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset))) => 236.75/34.88 (( 236.75/34.88 Y2 = Y1) | 236.75/34.88 (Y2 = Y0)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 subset( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 powerset( 236.75/34.88 binunion( 236.75/34.88 Y0, Y1))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 subset( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)), 236.75/34.88 powerset( 236.75/34.88 binunion( 236.75/34.88 Y0, Y1))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)), 236.75/34.88 powerset( 236.75/34.88 powerset( 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)), 236.75/34.88 powerset( 236.75/34.88 powerset( 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)), 236.75/34.88 cartprod( 236.75/34.88 Y0, Y1)))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 cartprod( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (??(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y0) & 236.75/34.88 (??(( 236.75/34.88 ^[Y4 : $i]: 236.75/34.88 (in(Y4, 236.75/34.88 Y1) & 236.75/34.88 (Y2 = 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 setadjoin( 236.75/34.88 Y4, 236.75/34.88 emptyset)), 236.75/34.88 emptyset))))))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 cartprod( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (??(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 setunion( 236.75/34.88 Y2)) & 236.75/34.88 (??(( 236.75/34.88 ^[Y4 : $i]: 236.75/34.88 (in(Y4, 236.75/34.88 setunion( 236.75/34.88 Y2)) & 236.75/34.88 (Y2 = 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 setadjoin( 236.75/34.88 Y4, 236.75/34.88 emptyset)), 236.75/34.88 emptyset))))))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (in(Y1, 236.75/34.88 setunion( 236.75/34.88 Y0)) => 236.75/34.88 (??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) & 236.75/34.88 in(Y1, 236.75/34.88 Y2)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 subset( 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset)), 236.75/34.88 Y0)))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 subset( 236.75/34.88 Y0, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset)))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (setunion( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset)) = 236.75/34.88 Y0)))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i > $o]: 236.75/34.88 (( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y0) => 236.75/34.88 (Y1(Y2) => 236.75/34.88 (Y1(Y3) => 236.75/34.88 (Y2 = Y3))))))))))) => 236.75/34.88 (( 236.75/34.88 ??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) & 236.75/34.88 Y1(Y2))))) => 236.75/34.88 (??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 dsetconstr( 236.75/34.88 Y0, Y1)) & 236.75/34.88 (dsetconstr( 236.75/34.88 Y0, Y1) = 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset)))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i > $o]: 236.75/34.88 (( 236.75/34.88 ??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 dsetconstr( 236.75/34.88 Y0, Y1)) & 236.75/34.88 (dsetconstr( 236.75/34.88 Y0, Y1) = 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset)))))) => 236.75/34.88 (??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) & 236.75/34.88 Y1(Y2)))))))))))) => 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i > $o]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (Y1(Y2) => 236.75/34.88 (( 236.75/34.88 !!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y0) => 236.75/34.88 (Y1(Y3) => 236.75/34.88 (Y3 = Y2)))))) => 236.75/34.88 (??(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 dsetconstr( 236.75/34.88 Y0, Y1)) & 236.75/34.88 (dsetconstr( 236.75/34.88 Y0, Y1) = 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.75/34.88 inference('lazy_cnf_imply', [status(thm)], ['187'])). 236.75/34.88 tff('189', plain, 236.75/34.88 ~ ((!!((^[Y0 : $i]: (~(in(Y0, emptyset)))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 ((??((^[Y1 : $i]: 236.75/34.88 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.88 (??(Y0)))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.75/34.88 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.88 (Y0 = Y1))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) => 236.75/34.88 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) => 236.75/34.88 (Y1(Y2) => 236.75/34.88 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.75/34.88 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y1) => 236.75/34.88 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.88 (!!((^[Y3 : $o]: 236.75/34.88 (((Y2 = Y0) => Y3) => 236.75/34.88 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, setadjoin(Y0, Y1)) => 236.75/34.88 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 ((!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y1) => in(Y2, Y0))))) => 236.75/34.88 in(Y1, powerset(Y0))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y1, powerset(Y0)) => 236.75/34.88 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y1, Y2) => 236.75/34.88 (in(Y2, Y0) => 236.75/34.88 in(Y1, setunion(Y0))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (in(Y1, setunion(Y0)) => 236.75/34.88 (!!((^[Y2 : $o]: 236.75/34.88 ((!!((^[Y3 : $i]: 236.75/34.88 (in(Y1, Y3) => 236.75/34.88 (in(Y3, Y0) => Y2))))) => 236.75/34.88 Y2))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (in(Y1, Y0) => 236.75/34.88 in(Y1, powerset(setunion(Y0)))))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 ((??((^[Y1 : $i]: 236.75/34.88 (Y0(Y1) & 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (Y0(Y2) => (Y1 = Y2))))))))) => 236.75/34.88 (??((^[Y1 : $i]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 ((Y0 != emptyset) => 236.75/34.88 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (in(Y0, setadjoin(Y1, emptyset)) => 236.75/34.88 (Y0 = Y1)))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 ((Y0 != Y1) => 236.75/34.88 (~(in(Y1, 236.75/34.88 setadjoin(Y0, emptyset))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 ((Y0 = Y1) => 236.75/34.88 in(Y0, 236.75/34.88 setadjoin(Y1, emptyset))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (in(Y0, 236.75/34.88 setadjoin(Y1, emptyset)) => 236.75/34.88 in(Y1, 236.75/34.88 setadjoin(Y0, emptyset))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setadjoin(Y0, 236.75/34.88 setadjoin(Y1, 236.75/34.88 emptyset))) => 236.75/34.88 ((Y2 = Y1) | 236.75/34.88 (Y2 = Y0)))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 in(Y0, 236.75/34.88 setadjoin(Y0, 236.75/34.88 setadjoin(Y1, emptyset))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 in(Y1, 236.75/34.88 setadjoin(Y0, 236.75/34.88 setadjoin(Y1, 236.75/34.88 emptyset))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 ((??((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) & 236.75/34.88 Y1(Y2))))) => 236.75/34.88 (dsetconstr(Y0, Y1) != 236.75/34.88 emptyset)))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (in(Y1, emptyset) => 236.75/34.88 Y0(Y1)))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 ((~((!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) => 236.75/34.88 Y1(Y2))))))) => 236.75/34.88 (??((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) & 236.75/34.88 (~(Y1(Y2)))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 ((!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) => 236.75/34.88 (~(Y1(Y2))))))) => 236.75/34.88 (~((??((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) & 236.75/34.88 Y1(Y2)))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 ((~((??((^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) & 236.75/34.88 Y1(Y2))))))) => 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) => 236.75/34.88 (~(Y1(Y2)))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 ((??((^[Y2 : $i]: 236.75/34.88 (in(Y2, Y0) & 236.75/34.88 (~(Y1(Y2))))))) => 236.75/34.88 (~((!!((^[Y2 : $i]: 236.75/34.88 ( 236.75/34.88 in(Y2, 236.75/34.88 Y0) => 236.75/34.88 Y1(Y2)))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $o]: 236.75/34.88 (Y0 => 236.75/34.88 in(emptyset, 236.75/34.88 prop2set(Y0)))))) => 236.75/34.88 ((!!((^[Y0 : $o]: 236.75/34.88 (Y0 => 236.75/34.88 set2prop(prop2set(Y0)))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 ((~((??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) & 236.75/34.88 Y1(Y2))))))) => 236.75/34.88 (!!((^[Y2 : $i]: 236.75/34.88 ( 236.75/34.88 in(Y2, 236.75/34.88 Y0) => 236.75/34.88 ( 236.75/34.88 ~( 236.75/34.88 Y1(Y2)))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 ((~((!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 ( 236.75/34.88 in(Y2, 236.75/34.88 Y0) => 236.75/34.88 Y1(Y2))))))) => 236.75/34.88 (??((^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) & 236.75/34.88 (~( 236.75/34.88 Y1(Y2)))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 ((??(Y0)) => 236.75/34.88 ((!!((^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y1) => 236.75/34.88 ( 236.75/34.88 Y0(Y2) => 236.75/34.88 ( 236.75/34.88 Y1 = Y2))))))))) => 236.75/34.88 (??((^[Y1 : $i]: 236.75/34.88 (Y0(Y1) & 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 ( 236.75/34.88 Y0(Y2) => 236.75/34.88 ( 236.75/34.88 Y1 = Y2)))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 ((??((^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y2) <=> 236.75/34.88 ( 236.75/34.88 Y2 = Y1)))))))) => 236.75/34.88 (??((^[Y1 : $i]: 236.75/34.88 (Y0(Y1) & 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 ( 236.75/34.88 Y0(Y2) => 236.75/34.88 ( 236.75/34.88 Y1 = Y2))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 ((Y0 = Y1) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (( 236.75/34.88 Y2 = Y3) => 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in(Y3, 236.75/34.88 Y1)))))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 ((Y0 = Y1) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (( 236.75/34.88 Y2 = Y3) => 236.75/34.88 (in(Y2, 236.75/34.88 Y0) <=> 236.75/34.88 in(Y3, 236.75/34.88 Y1)))))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 ((??((^[Y1 : $i]: 236.75/34.88 (Y0(Y1) & 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y2) => 236.75/34.88 (Y1 = Y2))))))))) => 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y1) => 236.75/34.88 (Y0(Y2) => 236.75/34.88 (Y1 = Y2))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 (!!((^[Y1 : $i > $o]: 236.75/34.88 (( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (( 236.75/34.88 Y2 = Y3) => 236.75/34.88 (Y0(Y2) <=> 236.75/34.88 Y1(Y3))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 ??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y2) & 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (Y0(Y3) => 236.75/34.88 (Y2 = Y3))))))))) <=> 236.75/34.88 ( 236.75/34.88 ??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y1(Y2) & 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (Y1(Y3) => 236.75/34.88 (Y2 = Y3))))))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 Y0 = Y1) => 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (( 236.75/34.88 Y2 = Y3) => 236.75/34.88 (setadjoin( 236.75/34.88 Y0, Y2) = 236.75/34.88 setadjoin( 236.75/34.88 Y1, Y3)))))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 Y0 = Y1) => 236.75/34.88 (powerset( 236.75/34.88 Y0) = 236.75/34.88 powerset( 236.75/34.88 Y1))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!((^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 Y0 = Y1) => 236.75/34.88 (setunion( 236.75/34.88 Y0) = 236.75/34.88 setunion( 236.75/34.88 Y1))))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 ((??(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 ( 236.75/34.88 Y0(Y1) & 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y2) => 236.75/34.88 (Y1 = Y2))))))))) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y1) => 236.75/34.88 (Y0(Y2) => 236.75/34.88 (Y1 = Y2))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i > $o]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i > $o]: 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (( 236.75/34.88 Y2 = Y3) => 236.75/34.88 (Y0(Y2) <=> 236.75/34.88 Y1(Y3))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 ??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y0(Y2) & 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (Y0(Y3) => 236.75/34.88 (Y2 = Y3))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 ??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (Y1(Y2) & 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (Y1(Y3) => 236.75/34.88 (Y2 = Y3))))))))) => 236.75/34.88 ( 236.75/34.88 descr(Y0) = 236.75/34.88 descr(Y1))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 Y0 = Y1) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i > $o]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i > $o]: 236.75/34.88 (( 236.75/34.88 !!(( 236.75/34.88 ^[Y4 : $i]: 236.75/34.88 (in(Y4, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y5 : $i]: 236.75/34.88 (in(Y5, 236.75/34.88 Y1) => 236.75/34.88 (( 236.75/34.88 Y4 = Y5) => 236.75/34.88 (Y2(Y4) <=> 236.75/34.88 Y3(Y5))))))))))) => 236.75/34.88 (dsetconstr( 236.75/34.88 Y0, Y2) = 236.75/34.88 dsetconstr( 236.75/34.88 Y1, Y3)))))))))))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in(Y2, 236.75/34.88 Y1))))) => 236.75/34.88 subset( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 Y0 = Y1) => 236.75/34.88 subset( 236.75/34.88 Y1, Y0)))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 Y0 = Y1) => 236.75/34.88 subset( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ((!!((^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 !!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in(Y2, 236.75/34.88 Y1))))) => 236.75/34.88 subset( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ((!!(subset( 236.75/34.88 emptyset))) => 236.75/34.88 ((!!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in(Y2, 236.75/34.88 Y1)))))))))))) => 236.75/34.88 ((!!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 Y0)))))))))))))) => 236.75/34.88 ((!!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 (~( 236.75/34.88 subset( 236.75/34.88 Y0, Y1)))))))))))))) => 236.75/34.88 (( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 subset( 236.75/34.88 Y0, Y1))) => 236.75/34.88 (Y0 != Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 (Y0 != Y1)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 subset( 236.75/34.88 Y0, Y0)))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 (subset( 236.75/34.88 Y1, Y2) => 236.75/34.88 subset( 236.75/34.88 Y0, Y2)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 subset( 236.75/34.88 Y1, 236.75/34.88 setadjoin( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y2) => 236.75/34.88 subset( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, Y2)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 in(Y0, 236.75/34.88 powerset( 236.75/34.88 Y1))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 (subset( 236.75/34.88 Y1, Y0) => 236.75/34.88 (Y0 = Y1))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, 236.75/34.88 emptyset) => 236.75/34.88 (Y0 = 236.75/34.88 emptyset))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y1, Y0) => 236.75/34.88 in(Y1, 236.75/34.88 powerset( 236.75/34.88 Y0))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (in(Y1, 236.75/34.88 powerset( 236.75/34.88 Y0)) => 236.75/34.88 subset( 236.75/34.88 Y1, Y0)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 in(Y0, 236.75/34.88 powerset( 236.75/34.88 Y0))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 subset( 236.75/34.88 powerset( 236.75/34.88 Y0), 236.75/34.88 powerset( 236.75/34.88 Y1))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i > $o]: 236.75/34.88 in( 236.75/34.88 dsetconstr( 236.75/34.88 Y0, Y1), 236.75/34.88 powerset( 236.75/34.88 Y0)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i > $o]: 236.75/34.88 subset( 236.75/34.88 dsetconstr( 236.75/34.88 Y0, Y1), 236.75/34.88 Y0))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in(Y2, 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 in(Y1, 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 in(Y2, 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $o]: 236.75/34.88 (in(Y2, 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (( 236.75/34.88 in(Y2, 236.75/34.88 Y0) => Y3) => 236.75/34.88 (( 236.75/34.88 in(Y2, 236.75/34.88 Y1) => Y3) => 236.75/34.88 Y3))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (in(Y2, 236.75/34.88 Y1) | 236.75/34.88 in(Y2, 236.75/34.88 Y0)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 subset( 236.75/34.88 Y0, 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 subset( 236.75/34.88 Y1, 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 in(Y2, 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y2, Y0) => 236.75/34.88 (subset( 236.75/34.88 Y2, Y1) => 236.75/34.88 subset( 236.75/34.88 Y2, 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1)) => 236.75/34.88 in(Y2, 236.75/34.88 Y0))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 subset( 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1), 236.75/34.88 Y0))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 (binintersect( 236.75/34.88 Y0, Y1) = 236.75/34.88 Y0)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1) = 236.75/34.88 Y1) => 236.75/34.88 subset( 236.75/34.88 Y1, Y0)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1)) => 236.75/34.88 in(Y2, 236.75/34.88 Y1))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 ~(( 236.75/34.88 ??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) & 236.75/34.88 in(Y2, 236.75/34.88 Y1))))))) => 236.75/34.88 (binintersect( 236.75/34.88 Y0, Y1) = 236.75/34.88 emptyset)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 subset( 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1), 236.75/34.88 Y1))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y1, Y0) => 236.75/34.88 (binintersect( 236.75/34.88 Y0, Y1) = 236.75/34.88 Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1) = 236.75/34.88 Y0) => 236.75/34.88 subset( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (binintersect( 236.75/34.88 Y0, 236.75/34.88 binunion( 236.75/34.88 Y1, Y2)) = 236.75/34.88 binunion( 236.75/34.88 binintersect( 236.75/34.88 Y0, Y1), 236.75/34.88 binintersect( 236.75/34.88 Y0, Y2)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)) => 236.75/34.88 in(Y2, 236.75/34.88 Y0))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (subset( 236.75/34.88 Y0, Y1) => 236.75/34.88 (setminus( 236.75/34.88 Y0, Y1) = 236.75/34.88 emptyset)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))) => 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in(Y2, 236.75/34.88 Y1)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 Y0)))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 setminus( 236.75/34.88 Y0, Y1)))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 subset( 236.75/34.88 setminus( 236.75/34.88 Y0, Y1), 236.75/34.88 Y0))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (( 236.75/34.88 setminus( 236.75/34.88 Y0, Y1) = 236.75/34.88 emptyset) => 236.75/34.88 subset( 236.75/34.88 Y0, Y1)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1)) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $o]: 236.75/34.88 (( 236.75/34.88 in(Y2, 236.75/34.88 Y0) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 Y3)) => 236.75/34.88 (( 236.75/34.88 ( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 ( 236.75/34.88 in(Y2, 236.75/34.88 Y1) => Y3)) => 236.75/34.88 Y3))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (in(Y2, 236.75/34.88 Y1) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y0))) => 236.75/34.88 (( 236.75/34.88 ~( 236.75/34.88 in(Y2, 236.75/34.88 Y1))) => 236.75/34.88 (~( 236.75/34.88 in(Y2, 236.75/34.88 symdiff( 236.75/34.88 Y0, Y1))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 in(Y1, 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 in(Y0, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 in(Y1, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (??(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)) = 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (??(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (??(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 setunion( 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)))) & 236.75/34.88 (setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset)), 236.75/34.88 emptyset)) = 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 setadjoin( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 emptyset))))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (in(Y1, 236.75/34.88 Y0) => 236.75/34.88 subset( 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset), 236.75/34.88 Y0)))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (in(Y1, 236.75/34.88 Y0) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset), 236.75/34.88 powerset( 236.75/34.88 Y0))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 emptyset), 236.75/34.88 powerset( 236.75/34.88 binunion( 236.75/34.88 Y0, Y1))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y0, 236.75/34.88 setadjoin( 236.75/34.88 Y1, 236.75/34.88 emptyset))) => 236.75/34.88 (( 236.75/34.88 Y2 = Y1) | 236.75/34.88 (Y2 = Y0)))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 subset( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.75/34.88 binunion( 236.75/34.88 Y0, Y1)))))))))))))))) => 236.75/34.88 ( 236.75/34.88 ( 236.75/34.88 !!(( 236.75/34.88 ^[Y0 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y1 : $i]: 236.75/34.88 (!!(( 236.75/34.88 ^[Y2 : $i]: 236.75/34.88 (in(Y2, 236.75/34.88 Y0) => 236.75/34.88 (!!(( 236.75/34.88 ^[Y3 : $i]: 236.75/34.88 (in(Y3, 236.75/34.88 Y1) => 236.75/34.88 in( 236.75/34.88 setadjoin( 236.75/34.88 Y2, 236.75/34.88 setadjoin( 236.75/34.88 Y3, 236.75/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 subset( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 cartprod( 236.86/34.88 Y0, Y1)))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 cartprod( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y0) & 236.86/34.88 (??(( 236.86/34.88 ^[Y4 : $i]: 236.86/34.88 (in(Y4, 236.86/34.88 Y1) & 236.86/34.88 (Y2 = 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 setadjoin( 236.86/34.88 Y4, 236.86/34.88 emptyset)), 236.86/34.88 emptyset))))))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 cartprod( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 setunion( 236.86/34.88 Y2)) & 236.86/34.88 (??(( 236.86/34.88 ^[Y4 : $i]: 236.86/34.88 (in(Y4, 236.86/34.88 setunion( 236.86/34.88 Y2)) & 236.86/34.88 (Y2 = 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 setadjoin( 236.86/34.88 Y4, 236.86/34.88 emptyset)), 236.86/34.88 emptyset))))))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (in(Y1, 236.86/34.88 setunion( 236.86/34.88 Y0)) => 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 in(Y1, 236.86/34.88 Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 subset( 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset)), 236.86/34.88 Y0)))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 subset( 236.86/34.88 Y0, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset)))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (setunion( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset)) = 236.86/34.88 Y0)))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y0) => 236.86/34.88 (Y1(Y2) => 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y2 = Y3))))))))))) => 236.86/34.88 (( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 Y1(Y2))))) => 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1)) & 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y1) = 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset)))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 (( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1)) & 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y1) = 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset)))))) => 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 Y1(Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (Y1(Y2) => 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y0) => 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y3 = Y2)))))) => 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1)) & 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y1) = 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.88 inference('lazy_cnf_imply', [status(thm)], ['188'])). 236.86/34.88 tff('190', plain, 236.86/34.88 ~ ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.88 (??(Y0)))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.86/34.88 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.88 (Y0 = Y1))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (Y1(Y2) => 236.86/34.88 (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.88 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.88 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y1) => 236.86/34.88 in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.88 (!!((^[Y3 : $o]: 236.86/34.88 (((Y2 = Y0) => Y3) => 236.86/34.88 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.88 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.88 in(Y1, powerset(Y0))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y1, powerset(Y0)) => 236.86/34.88 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y1, Y2) => 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 in(Y1, setunion(Y0))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y1, setunion(Y0)) => 236.86/34.88 (!!((^[Y2 : $o]: 236.86/34.88 ((!!((^[Y3 : $i]: 236.86/34.88 (in(Y1, Y3) => 236.86/34.88 (in(Y3, Y0) => Y2))))) => 236.86/34.88 Y2))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y1, Y0) => 236.86/34.88 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.88 (??((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((Y0 != emptyset) => 236.86/34.88 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.88 (Y0 = Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 != Y1) => 236.86/34.88 (~(in(Y1, 236.86/34.88 setadjoin(Y0, emptyset))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 = Y1) => 236.86/34.88 in(Y0, 236.86/34.88 setadjoin(Y1, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y0, 236.86/34.88 setadjoin(Y1, emptyset)) => 236.86/34.88 in(Y1, 236.86/34.88 setadjoin(Y0, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 setadjoin(Y0, 236.86/34.88 setadjoin(Y1, 236.86/34.88 emptyset))) => 236.86/34.88 ((Y2 = Y1) | 236.86/34.88 (Y2 = Y0)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 in(Y0, 236.86/34.88 setadjoin(Y0, 236.86/34.88 setadjoin(Y1, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 in(Y1, 236.86/34.88 setadjoin(Y0, 236.86/34.88 setadjoin(Y1, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 Y1(Y2))))) => 236.86/34.88 (dsetconstr(Y0, Y1) != 236.86/34.88 emptyset)))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y1, emptyset) => 236.86/34.88 Y0(Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 (~(Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (~(Y1(Y2))))))) => 236.86/34.88 (~((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (~(Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 (~(Y1(Y2))))))) => 236.86/34.88 (~((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $o]: 236.86/34.88 (Y0 => 236.86/34.88 in(emptyset, prop2set(Y0)))))) => 236.86/34.88 ((!!((^[Y0 : $o]: 236.86/34.88 (Y0 => 236.86/34.88 set2prop(prop2set(Y0)))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 ( 236.86/34.88 ~( 236.86/34.88 Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (??((^[Y2 : $i]: 236.86/34.88 ( 236.86/34.88 in(Y2, 236.86/34.88 Y0) & 236.86/34.88 ( 236.86/34.88 ~( 236.86/34.88 Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??(Y0)) => 236.86/34.88 ((!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y1) => 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))) => 236.86/34.88 (??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 ( 236.86/34.88 Y1 = Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) <=> 236.86/34.88 (Y2 = Y1)))))))) => 236.86/34.88 (??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 ( 236.86/34.88 Y1 = Y2))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 = Y1) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y3, 236.86/34.88 Y1)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 = Y1) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (in(Y2, 236.86/34.88 Y0) <=> 236.86/34.88 in(Y3, 236.86/34.88 Y1)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))) => 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y1) => 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (Y0(Y2) <=> 236.86/34.88 Y1(Y3))))))))) => 236.86/34.88 (( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y0(Y3) => 236.86/34.88 (Y2 = Y3))))))))) <=> 236.86/34.88 ( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y1(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y2 = Y3))))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (setadjoin( 236.86/34.88 Y0, Y2) = 236.86/34.88 setadjoin( 236.86/34.88 Y1, Y3)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 Y0 = Y1) => 236.86/34.88 ( 236.86/34.88 powerset( 236.86/34.88 Y0) = 236.86/34.88 powerset( 236.86/34.88 Y1))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 (setunion( 236.86/34.88 Y0) = 236.86/34.88 setunion( 236.86/34.88 Y1))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y1) => 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (Y0(Y2) <=> 236.86/34.88 Y1(Y3))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y0(Y3) => 236.86/34.88 (Y2 = Y3))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y1(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y2 = Y3))))))))) => 236.86/34.88 ( 236.86/34.88 descr(Y0) = 236.86/34.88 descr(Y1))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 Y0 = Y1) => 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i > $o]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i > $o]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y4 : $i]: 236.86/34.88 (in(Y4, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y5 : $i]: 236.86/34.88 (in(Y5, 236.86/34.88 Y1) => 236.86/34.88 (( 236.86/34.88 Y4 = Y5) => 236.86/34.88 (Y2(Y4) <=> 236.86/34.88 Y3(Y5))))))))))) => 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y2) = 236.86/34.88 dsetconstr( 236.86/34.88 Y1, Y3)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 Y1))))) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 subset( 236.86/34.88 Y1, Y0)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 Y1))))) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ((!!(subset( 236.86/34.88 emptyset))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 Y1)))))))))))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 Y0)))))))))))))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (~( 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))))))))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 subset( 236.86/34.88 Y0, Y1))) => 236.86/34.88 (Y0 != Y1)))))))) => 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (Y0 != Y1)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 subset( 236.86/34.88 Y0, Y0)))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (subset( 236.86/34.88 Y1, Y2) => 236.86/34.88 subset( 236.86/34.88 Y0, Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 Y1, 236.86/34.88 setadjoin( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y2) => 236.86/34.88 subset( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 in(Y0, 236.86/34.88 powerset( 236.86/34.88 Y1))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (subset( 236.86/34.88 Y1, Y0) => 236.86/34.88 (Y0 = Y1))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, 236.86/34.88 emptyset) => 236.86/34.88 (Y0 = 236.86/34.88 emptyset))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y1, Y0) => 236.86/34.88 in(Y1, 236.86/34.88 powerset( 236.86/34.88 Y0))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (in(Y1, 236.86/34.88 powerset( 236.86/34.88 Y0)) => 236.86/34.88 subset( 236.86/34.88 Y1, Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 in(Y0, 236.86/34.88 powerset( 236.86/34.88 Y0))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 subset( 236.86/34.88 powerset( 236.86/34.88 Y0), 236.86/34.88 powerset( 236.86/34.88 Y1))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 in( 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1), 236.86/34.88 powerset( 236.86/34.88 Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 subset( 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1), 236.86/34.88 Y0))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 in(Y1, 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y1) => 236.86/34.88 in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $o]: 236.86/34.88 (in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (( 236.86/34.88 in(Y2, 236.86/34.88 Y0) => Y3) => 236.86/34.88 (( 236.86/34.88 in(Y2, 236.86/34.88 Y1) => Y3) => 236.86/34.88 Y3))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (in(Y2, 236.86/34.88 Y1) | 236.86/34.88 in(Y2, 236.86/34.88 Y0)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 Y0, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 Y1, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (in(Y2, 236.86/34.88 Y1) => 236.86/34.88 in(Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y2, Y0) => 236.86/34.88 (subset( 236.86/34.88 Y2, Y1) => 236.86/34.88 subset( 236.86/34.88 Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1)) => 236.86/34.88 in(Y2, 236.86/34.88 Y0))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1), 236.86/34.88 Y0))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 Y1) => 236.86/34.88 subset( 236.86/34.88 Y1, Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1)) => 236.86/34.88 in(Y2, 236.86/34.88 Y1))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 ~(( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 in(Y2, 236.86/34.88 Y1))))))) => 236.86/34.88 (binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 emptyset)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1), 236.86/34.88 Y1))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y1, Y0) => 236.86/34.88 (binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 Y0) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (binintersect( 236.86/34.88 Y0, 236.86/34.88 binunion( 236.86/34.88 Y1, Y2)) = 236.86/34.88 binunion( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1), 236.86/34.88 binintersect( 236.86/34.88 Y0, Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 in(Y2, 236.86/34.88 setminus( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 setminus( 236.86/34.88 Y0, Y1)) => 236.86/34.88 in(Y2, 236.86/34.88 Y0))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 setminus( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (setminus( 236.86/34.88 Y0, Y1) = 236.86/34.88 emptyset)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 setminus( 236.86/34.88 Y0, Y1)))) => 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 Y1)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 setminus( 236.86/34.88 Y0, Y1)))) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 Y0)))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y0))) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 setminus( 236.86/34.88 Y0, Y1)))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y1) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 setminus( 236.86/34.88 Y0, Y1)))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 setminus( 236.86/34.88 Y0, Y1), 236.86/34.88 Y0))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 setminus( 236.86/34.88 Y0, Y1) = 236.86/34.88 emptyset) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 symdiff( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $o]: 236.86/34.88 (( 236.86/34.88 in(Y2, 236.86/34.88 Y0) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 Y3)) => 236.86/34.88 (( 236.86/34.88 ( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y0))) => 236.86/34.88 ( 236.86/34.88 in(Y2, 236.86/34.88 Y1) => Y3)) => 236.86/34.88 Y3))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 in(Y2, 236.86/34.88 symdiff( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y0))) => 236.86/34.88 (in(Y2, 236.86/34.88 Y1) => 236.86/34.88 in(Y2, 236.86/34.88 symdiff( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (in(Y2, 236.86/34.88 Y1) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 symdiff( 236.86/34.88 Y0, Y1))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y0))) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 symdiff( 236.86/34.88 Y0, Y1))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 in(Y1, 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 in(Y0, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 in(Y1, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)))) & 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)))) & 236.86/34.88 (setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)) = 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)))) & 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)))) & 236.86/34.88 (setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)) = 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (in(Y1, 236.86/34.88 Y0) => 236.86/34.88 subset( 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset), 236.86/34.88 Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (in(Y1, 236.86/34.88 Y0) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset), 236.86/34.88 powerset( 236.86/34.88 Y0))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset))) => 236.86/34.88 (( 236.86/34.88 Y2 = Y1) | 236.86/34.88 (Y2 = Y0)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 subset( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 subset( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 powerset( 236.86/34.88 powerset( 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y1) => 236.86/34.88 in( 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)), 236.86/34.88 emptyset)), 236.86/34.88 cartprod( 236.86/34.88 Y0, Y1)))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 cartprod( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y0) & 236.86/34.88 (??(( 236.86/34.88 ^[Y4 : $i]: 236.86/34.88 (in(Y4, 236.86/34.88 Y1) & 236.86/34.88 (Y2 = 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 setadjoin( 236.86/34.88 Y4, 236.86/34.88 emptyset)), 236.86/34.88 emptyset))))))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 cartprod( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 setunion( 236.86/34.88 Y2)) & 236.86/34.88 (??(( 236.86/34.88 ^[Y4 : $i]: 236.86/34.88 (in(Y4, 236.86/34.88 setunion( 236.86/34.88 Y2)) & 236.86/34.88 (Y2 = 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset), 236.86/34.88 setadjoin( 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 setadjoin( 236.86/34.88 Y4, 236.86/34.88 emptyset)), 236.86/34.88 emptyset))))))))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (in(Y1, 236.86/34.88 setunion( 236.86/34.88 Y0)) => 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 in(Y1, 236.86/34.88 Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 subset( 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset)), 236.86/34.88 Y0)))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 subset( 236.86/34.88 Y0, 236.86/34.88 setunion( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset)))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (setunion( 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 emptyset)) = 236.86/34.88 Y0)))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y0) => 236.86/34.88 (Y1(Y2) => 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y2 = Y3))))))))))) => 236.86/34.88 (( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 Y1(Y2))))) => 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1)) & 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y1) = 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset)))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 (( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1)) & 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y1) = 236.86/34.88 setadjoin( 236.86/34.88 Y2, 236.86/34.88 emptyset)))))) => 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 Y1(Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (Y1(Y2) => 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 Y0) => 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y3 = Y2)))))) => 236.86/34.88 (??(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (in(Y3, 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1)) & 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y1) = 236.86/34.88 setadjoin( 236.86/34.88 Y3, 236.86/34.88 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.88 inference('lazy_cnf_imply', [status(thm)], ['189'])). 236.86/34.88 tff('191', plain, 236.86/34.88 ~ ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 236.86/34.88 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.88 (Y0 = Y1))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.88 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.88 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.88 (!!((^[Y3 : $o]: 236.86/34.88 (((Y2 = Y0) => Y3) => 236.86/34.88 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.88 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.88 in(Y1, powerset(Y0))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.88 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y1, powerset(Y0)) => 236.86/34.88 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y1, Y2) => 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 in(Y1, setunion(Y0))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y1, setunion(Y0)) => 236.86/34.88 (!!((^[Y2 : $o]: 236.86/34.88 ((!!((^[Y3 : $i]: 236.86/34.88 (in(Y1, Y3) => 236.86/34.88 (in(Y3, Y0) => Y2))))) => 236.86/34.88 Y2))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y1, Y0) => 236.86/34.88 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.88 (??((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ((Y0 != emptyset) => 236.86/34.88 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.88 (Y0 = Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 != Y1) => 236.86/34.88 (~(in(Y1, 236.86/34.88 setadjoin(Y0, emptyset))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 = Y1) => 236.86/34.88 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y0, 236.86/34.88 setadjoin(Y1, emptyset)) => 236.86/34.88 in(Y1, 236.86/34.88 setadjoin(Y0, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 setadjoin(Y0, 236.86/34.88 setadjoin(Y1, 236.86/34.88 emptyset))) => 236.86/34.88 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 in(Y0, 236.86/34.88 setadjoin(Y0, 236.86/34.88 setadjoin(Y1, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 in(Y1, 236.86/34.88 setadjoin(Y0, 236.86/34.88 setadjoin(Y1, emptyset))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 Y1(Y2))))) => 236.86/34.88 (dsetconstr(Y0, Y1) != 236.86/34.88 emptyset)))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (in(Y1, emptyset) => 236.86/34.88 Y0(Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 (~(Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (~(Y1(Y2))))))) => 236.86/34.88 (~((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (~(Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) & 236.86/34.88 (~(Y1(Y2))))))) => 236.86/34.88 (~((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $o]: 236.86/34.88 (Y0 => 236.86/34.88 in(emptyset, prop2set(Y0)))))) => 236.86/34.88 ((!!((^[Y0 : $o]: 236.86/34.88 (Y0 => 236.86/34.88 set2prop(prop2set(Y0)))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((??((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, Y0) => 236.86/34.88 (~(Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((~((!!((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 Y1(Y2))))))) => 236.86/34.88 (??((^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 ( 236.86/34.88 ~( 236.86/34.88 Y1(Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??(Y0)) => 236.86/34.88 ((!!((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y1) => 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))) => 236.86/34.88 (??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2)))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) <=> 236.86/34.88 (Y2 = Y1)))))))) => 236.86/34.88 (??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 = Y1) => 236.86/34.88 (!!((^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y3, 236.86/34.88 Y1)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 = Y1) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (in(Y2, 236.86/34.88 Y0) <=> 236.86/34.88 in(Y3, 236.86/34.88 Y1)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))) => 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 ( 236.86/34.88 Y0(Y1) => 236.86/34.88 ( 236.86/34.88 Y0(Y2) => 236.86/34.88 ( 236.86/34.88 Y1 = Y2))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 ((!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (Y0(Y2) <=> 236.86/34.88 Y1(Y3))))))))) => 236.86/34.88 ((??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y0(Y3) => 236.86/34.88 (Y2 = Y3))))))))) <=> 236.86/34.88 (??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y1(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y2 = Y3))))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ((Y0 = Y1) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (setadjoin( 236.86/34.88 Y0, Y2) = 236.86/34.88 setadjoin( 236.86/34.88 Y1, Y3)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 ( 236.86/34.88 powerset( 236.86/34.88 Y0) = 236.86/34.88 powerset( 236.86/34.88 Y1))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 Y0 = Y1) => 236.86/34.88 ( 236.86/34.88 setunion( 236.86/34.88 Y0) = 236.86/34.88 setunion( 236.86/34.88 Y1))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 ((??((^[Y1 : $i]: 236.86/34.88 (Y0(Y1) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))) => 236.86/34.88 (!!((^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y1) => 236.86/34.88 (Y0(Y2) => 236.86/34.88 (Y1 = Y2))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i > $o]: 236.86/34.88 (!!((^[Y1 : $i > $o]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (( 236.86/34.88 Y2 = Y3) => 236.86/34.88 (Y0(Y2) <=> 236.86/34.88 Y1(Y3))))))))) => 236.86/34.88 (( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y0(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y0(Y3) => 236.86/34.88 (Y2 = Y3))))))))) => 236.86/34.88 (( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (Y1(Y2) & 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i]: 236.86/34.88 (Y1(Y3) => 236.86/34.88 (Y2 = Y3))))))))) => 236.86/34.88 (descr( 236.86/34.88 Y0) = 236.86/34.88 descr(Y1))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i > $o]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $i > $o]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y4 : $i]: 236.86/34.88 (in(Y4, 236.86/34.88 Y0) => 236.86/34.88 (!!(( 236.86/34.88 ^[Y5 : $i]: 236.86/34.88 (in(Y5, 236.86/34.88 Y1) => 236.86/34.88 (( 236.86/34.88 Y4 = Y5) => 236.86/34.88 (Y2(Y4) <=> 236.86/34.88 Y3(Y5))))))))))) => 236.86/34.88 (dsetconstr( 236.86/34.88 Y0, Y2) = 236.86/34.88 dsetconstr( 236.86/34.88 Y1, Y3)))))))))))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 Y1))))) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 subset( 236.86/34.88 Y1, Y0)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 Y0 = Y1) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 Y1))))) => 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ((!!(subset( 236.86/34.88 emptyset))) => 236.86/34.88 ((!!((^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 Y1)))))))))))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (~( 236.86/34.88 in(Y2, 236.86/34.88 Y0)))))))))))))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (~( 236.86/34.88 subset( 236.86/34.88 Y0, Y1)))))))))))))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 subset( 236.86/34.88 Y0, Y1))) => 236.86/34.88 (Y0 != Y1)))))))) => 236.86/34.88 ((!!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (( 236.86/34.88 ~( 236.86/34.88 in(Y2, 236.86/34.88 Y1))) => 236.86/34.88 (Y0 != Y1)))))))))))) => 236.86/34.88 (( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 subset( 236.86/34.88 Y0, Y0)))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (subset( 236.86/34.88 Y1, Y2) => 236.86/34.88 subset( 236.86/34.88 Y0, Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 Y1, 236.86/34.88 setadjoin( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y2) => 236.86/34.88 subset( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, Y2)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 in(Y0, 236.86/34.88 powerset( 236.86/34.88 Y1))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (subset( 236.86/34.88 Y1, Y0) => 236.86/34.88 (Y0 = Y1))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, 236.86/34.88 emptyset) => 236.86/34.88 (Y0 = 236.86/34.88 emptyset))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y1, Y0) => 236.86/34.88 in(Y1, 236.86/34.88 powerset( 236.86/34.88 Y0))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (in(Y1, 236.86/34.88 powerset( 236.86/34.88 Y0)) => 236.86/34.88 subset( 236.86/34.88 Y1, Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 in(Y0, 236.86/34.88 powerset( 236.86/34.88 Y0))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 subset( 236.86/34.88 powerset( 236.86/34.88 Y0), 236.86/34.88 powerset( 236.86/34.88 Y1))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 in( 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1), 236.86/34.88 powerset( 236.86/34.88 Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i > $o]: 236.86/34.88 subset( 236.86/34.88 dsetconstr( 236.86/34.88 Y0, Y1), 236.86/34.88 Y0))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 in(Y1, 236.86/34.88 setadjoin( 236.86/34.88 Y0, 236.86/34.88 setadjoin( 236.86/34.88 Y1, 236.86/34.88 emptyset))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y1) => 236.86/34.88 in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y3 : $o]: 236.86/34.88 (in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (( 236.86/34.88 in(Y2, 236.86/34.88 Y0) => Y3) => 236.86/34.88 (( 236.86/34.88 in(Y2, 236.86/34.88 Y1) => Y3) => 236.86/34.88 Y3))))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)) => 236.86/34.88 (in(Y2, 236.86/34.88 Y1) | 236.86/34.88 in(Y2, 236.86/34.88 Y0)))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 Y0, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 Y1, 236.86/34.88 binunion( 236.86/34.88 Y0, Y1)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) => 236.86/34.88 (in(Y2, 236.86/34.88 Y1) => 236.86/34.88 in(Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y2, Y0) => 236.86/34.88 (subset( 236.86/34.88 Y2, Y1) => 236.86/34.88 subset( 236.86/34.88 Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1))))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1)) => 236.86/34.88 in(Y2, 236.86/34.88 Y0))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1), 236.86/34.88 Y0))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y0, Y1) => 236.86/34.88 (binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 Y1) => 236.86/34.88 subset( 236.86/34.88 Y1, Y0)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1)) => 236.86/34.88 in(Y2, 236.86/34.88 Y1))))))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (( 236.86/34.88 ~(( 236.86/34.88 ??(( 236.86/34.88 ^[Y2 : $i]: 236.86/34.88 (in(Y2, 236.86/34.88 Y0) & 236.86/34.88 in(Y2, 236.86/34.88 Y1))))))) => 236.86/34.88 (binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 emptyset)))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 subset( 236.86/34.88 binintersect( 236.86/34.88 Y0, Y1), 236.86/34.88 Y1))))))) => 236.86/34.88 ( 236.86/34.88 ( 236.86/34.88 !!(( 236.86/34.88 ^[Y0 : $i]: 236.86/34.88 (!!(( 236.86/34.88 ^[Y1 : $i]: 236.86/34.88 (subset( 236.86/34.88 Y1, Y0) => 236.86/34.88 (binintersect( 236.86/34.88 Y0, Y1) = 236.86/34.88 Y1)))))))) => 236.86/34.88 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y0) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (binintersect( 236.86/34.89 Y0, 236.86/34.89 binunion( 236.86/34.89 Y1, Y2)) = 236.86/34.89 binunion( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 binintersect( 236.86/34.89 Y0, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y0))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $o]: 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 Y3)) => 236.86/34.89 (( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 ( 236.86/34.89 in(Y2, 236.86/34.89 Y1) => Y3)) => 236.86/34.89 Y3))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)) = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)) = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 Y0) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset), 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 Y0) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset), 236.86/34.89 powerset( 236.86/34.89 Y0))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))) => 236.86/34.89 (( 236.86/34.89 Y2 = Y1) | 236.86/34.89 (Y2 = Y0)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) & 236.86/34.89 (??(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 Y1) & 236.86/34.89 (Y2 = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 setadjoin( 236.86/34.89 Y4, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 Y2)) & 236.86/34.89 (??(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 setunion( 236.86/34.89 Y2)) & 236.86/34.89 (Y2 = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 setadjoin( 236.86/34.89 Y4, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 setunion( 236.86/34.89 Y0)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 in(Y1, 236.86/34.89 Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)), 236.86/34.89 Y0)))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)) = 236.86/34.89 Y0)))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y2) => 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))))) => 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset)))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y2) => 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y3 = Y2)))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.89 inference('lazy_cnf_imply', [status(thm)], ['190'])). 236.86/34.89 tff('192', plain, 236.86/34.89 ~ ((!!((^[Y0 : $i]: 236.86/34.89 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.89 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.89 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.89 (!!((^[Y3 : $o]: 236.86/34.89 (((Y2 = Y0) => Y3) => 236.86/34.89 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.89 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.89 in(Y1, powerset(Y0))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y1, powerset(Y0)) => 236.86/34.89 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y1, Y2) => 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 in(Y1, setunion(Y0))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, setunion(Y0)) => 236.86/34.89 (!!((^[Y2 : $o]: 236.86/34.89 ((!!((^[Y3 : $i]: 236.86/34.89 (in(Y1, Y3) => 236.86/34.89 (in(Y3, Y0) => Y2))))) => 236.86/34.89 Y2))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, Y0) => 236.86/34.89 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((Y0 != emptyset) => 236.86/34.89 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.89 (Y0 = Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 != Y1) => 236.86/34.89 (~(in(Y1, 236.86/34.89 setadjoin(Y0, emptyset))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.89 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, 236.86/34.89 emptyset))) => 236.86/34.89 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.89 (dsetconstr(Y0, Y1) != 236.86/34.89 emptyset)))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2))))))) => 236.86/34.89 (~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2))))))) => 236.86/34.89 (~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $o]: 236.86/34.89 (Y0 => 236.86/34.89 in(emptyset, prop2set(Y0)))))) => 236.86/34.89 ((!!((^[Y0 : $o]: 236.86/34.89 (Y0 => 236.86/34.89 set2prop(prop2set(Y0)))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((??((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??(Y0)) => 236.86/34.89 ((!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 Y0(Y1) => 236.86/34.89 ( 236.86/34.89 Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 Y0(Y2) <=> 236.86/34.89 ( 236.86/34.89 Y2 = Y1)))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y3, 236.86/34.89 Y1)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) <=> 236.86/34.89 in(Y3, 236.86/34.89 Y1)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))) => 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 ( 236.86/34.89 Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 Y1(Y3))))))))) => 236.86/34.89 ((??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y0(Y3) => 236.86/34.89 (Y2 = Y3))))))))) <=> 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y1(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (setadjoin( 236.86/34.89 Y0, Y2) = 236.86/34.89 setadjoin( 236.86/34.89 Y1, Y3)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (powerset( 236.86/34.89 Y0) = 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 Y0 = Y1) => 236.86/34.89 ( 236.86/34.89 setunion( 236.86/34.89 Y0) = 236.86/34.89 setunion( 236.86/34.89 Y1))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))) => 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 Y1(Y3))))))))) => 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y0(Y3) => 236.86/34.89 (Y2 = Y3))))))))) => 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y1(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))) => 236.86/34.89 (descr( 236.86/34.89 Y0) = 236.86/34.89 descr(Y1))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 Y0 = Y1) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i > $o]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y5 : $i]: 236.86/34.89 (in(Y5, 236.86/34.89 Y1) => 236.86/34.89 (( 236.86/34.89 Y4 = Y5) => 236.86/34.89 (Y2(Y4) <=> 236.86/34.89 Y3(Y5))))))))))) => 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y2) = 236.86/34.89 dsetconstr( 236.86/34.89 Y1, Y3)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 Y0 = Y1) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 Y0 = Y1) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!(subset( 236.86/34.89 emptyset))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 subset( 236.86/34.89 Y0, Y1))) => 236.86/34.89 (Y0 != Y1)))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (Y0 != Y1)))))))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, Y0)))) => 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (subset( 236.86/34.89 Y1, Y2) => 236.86/34.89 subset( 236.86/34.89 Y0, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y2) => 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 in(Y0, 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 (Y0 = Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, 236.86/34.89 emptyset) => 236.86/34.89 (Y0 = 236.86/34.89 emptyset))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 in(Y1, 236.86/34.89 powerset( 236.86/34.89 Y0))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 powerset( 236.86/34.89 Y0)) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 powerset( 236.86/34.89 Y0))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 subset( 236.86/34.89 powerset( 236.86/34.89 Y0), 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 in( 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1), 236.86/34.89 powerset( 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 subset( 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $o]: 236.86/34.89 (in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => Y3) => 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y1) => Y3) => 236.86/34.89 Y3))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) | 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y1, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y2, Y0) => 236.86/34.89 (subset( 236.86/34.89 Y2, Y1) => 236.86/34.89 subset( 236.86/34.89 Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y0))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 ~(( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 Y1))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y0) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (binintersect( 236.86/34.89 Y0, 236.86/34.89 binunion( 236.86/34.89 Y1, Y2)) = 236.86/34.89 binunion( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 binintersect( 236.86/34.89 Y0, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y0))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $o]: 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 Y3)) => 236.86/34.89 (( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 ( 236.86/34.89 in(Y2, 236.86/34.89 Y1) => Y3)) => 236.86/34.89 Y3))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)) = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)) = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 Y0) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset), 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 Y0) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset), 236.86/34.89 powerset( 236.86/34.89 Y0))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))) => 236.86/34.89 (( 236.86/34.89 Y2 = Y1) | 236.86/34.89 (Y2 = Y0)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) & 236.86/34.89 (??(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 Y1) & 236.86/34.89 (Y2 = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 setadjoin( 236.86/34.89 Y4, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 Y2)) & 236.86/34.89 (??(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 setunion( 236.86/34.89 Y2)) & 236.86/34.89 (Y2 = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 setadjoin( 236.86/34.89 Y4, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 setunion( 236.86/34.89 Y0)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 in(Y1, 236.86/34.89 Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)), 236.86/34.89 Y0)))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)) = 236.86/34.89 Y0)))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y2) => 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))))) => 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset)))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y2) => 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y3 = Y2)))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.89 inference('lazy_cnf_imply', [status(thm)], ['191'])). 236.86/34.89 tff('193', plain, 236.86/34.89 ~ ((!!((^[Y0 : $i]: 236.86/34.89 ((!!((^[Y1 : $i]: (~(in(Y1, Y0)))))) => (Y0 = emptyset))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.89 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.89 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.89 (!!((^[Y3 : $o]: 236.86/34.89 (((Y2 = Y0) => Y3) => 236.86/34.89 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.89 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.89 in(Y1, powerset(Y0))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y1, powerset(Y0)) => 236.86/34.89 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y1, Y2) => 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 in(Y1, setunion(Y0))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, setunion(Y0)) => 236.86/34.89 (!!((^[Y2 : $o]: 236.86/34.89 ((!!((^[Y3 : $i]: 236.86/34.89 (in(Y1, Y3) => 236.86/34.89 (in(Y3, Y0) => Y2))))) => 236.86/34.89 Y2))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, Y0) => 236.86/34.89 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((Y0 != emptyset) => 236.86/34.89 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.89 (Y0 = Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 != Y1) => 236.86/34.89 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.89 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, 236.86/34.89 emptyset))) => 236.86/34.89 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.89 (dsetconstr(Y0, Y1) != 236.86/34.89 emptyset)))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2))))))) => 236.86/34.89 (~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2))))))) => 236.86/34.89 (~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $o]: 236.86/34.89 (Y0 => 236.86/34.89 in(emptyset, prop2set(Y0)))))) => 236.86/34.89 ((!!((^[Y0 : $o]: 236.86/34.89 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((!!((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??(Y0)) => 236.86/34.89 ((!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 ( 236.86/34.89 Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 ( 236.86/34.89 Y2 = Y1)))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y3, 236.86/34.89 Y1)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) <=> 236.86/34.89 in(Y3, 236.86/34.89 Y1)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))) => 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 Y1(Y3))))))))) => 236.86/34.89 ((??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 Y0(Y2) & 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y0(Y3) => 236.86/34.89 (Y2 = Y3))))))))) <=> 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 Y1(Y2) & 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (setadjoin( 236.86/34.89 Y0, Y2) = 236.86/34.89 setadjoin( 236.86/34.89 Y1, Y3)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (powerset( 236.86/34.89 Y0) = 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (setunion( 236.86/34.89 Y0) = 236.86/34.89 setunion( 236.86/34.89 Y1))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 ( 236.86/34.89 Y0(Y1) & 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))) => 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 Y1(Y3))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y0(Y3) => 236.86/34.89 (Y2 = Y3))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y1(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))) => 236.86/34.89 ( 236.86/34.89 descr(Y0) = 236.86/34.89 descr(Y1))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 Y0 = Y1) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i > $o]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y5 : $i]: 236.86/34.89 (in(Y5, 236.86/34.89 Y1) => 236.86/34.89 (( 236.86/34.89 Y4 = Y5) => 236.86/34.89 (Y2(Y4) <=> 236.86/34.89 Y3(Y5))))))))))) => 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y2) = 236.86/34.89 dsetconstr( 236.86/34.89 Y1, Y3)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 Y0 = Y1) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 Y0 = Y1) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!(subset( 236.86/34.89 emptyset))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 subset( 236.86/34.89 Y0, Y1))) => 236.86/34.89 (Y0 != Y1)))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (Y0 != Y1)))))))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, Y0)))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (subset( 236.86/34.89 Y1, Y2) => 236.86/34.89 subset( 236.86/34.89 Y0, Y2)))))))))))) => 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y2) => 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 in(Y0, 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 (Y0 = Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, 236.86/34.89 emptyset) => 236.86/34.89 (Y0 = 236.86/34.89 emptyset))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 in(Y1, 236.86/34.89 powerset( 236.86/34.89 Y0))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 powerset( 236.86/34.89 Y0)) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 powerset( 236.86/34.89 Y0))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 subset( 236.86/34.89 powerset( 236.86/34.89 Y0), 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 in( 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1), 236.86/34.89 powerset( 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 subset( 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $o]: 236.86/34.89 (in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => Y3) => 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y1) => Y3) => 236.86/34.89 Y3))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) | 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y1, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y2, Y0) => 236.86/34.89 (subset( 236.86/34.89 Y2, Y1) => 236.86/34.89 subset( 236.86/34.89 Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y0))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 ~(( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 Y1))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y0) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (binintersect( 236.86/34.89 Y0, 236.86/34.89 binunion( 236.86/34.89 Y1, Y2)) = 236.86/34.89 binunion( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 binintersect( 236.86/34.89 Y0, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y0))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $o]: 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 Y3)) => 236.86/34.89 (( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 ( 236.86/34.89 in(Y2, 236.86/34.89 Y1) => Y3)) => 236.86/34.89 Y3))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)) = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)))) & 236.86/34.89 (setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)) = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 Y0) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset), 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 Y0) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset), 236.86/34.89 powerset( 236.86/34.89 Y0))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))) => 236.86/34.89 (( 236.86/34.89 Y2 = Y1) | 236.86/34.89 (Y2 = Y0)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 powerset( 236.86/34.89 powerset( 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y1) => 236.86/34.89 in( 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset)), 236.86/34.89 emptyset)), 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) & 236.86/34.89 (??(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 Y1) & 236.86/34.89 (Y2 = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 setadjoin( 236.86/34.89 Y4, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 cartprod( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 setunion( 236.86/34.89 Y2)) & 236.86/34.89 (??(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 setunion( 236.86/34.89 Y2)) & 236.86/34.89 (Y2 = 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset), 236.86/34.89 setadjoin( 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 setadjoin( 236.86/34.89 Y4, 236.86/34.89 emptyset)), 236.86/34.89 emptyset))))))))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 setunion( 236.86/34.89 Y0)) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 in(Y1, 236.86/34.89 Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)), 236.86/34.89 Y0)))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (setunion( 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 emptyset)) = 236.86/34.89 Y0)))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y2) => 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))))) => 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y2, 236.86/34.89 emptyset)))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 Y1(Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y2) => 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 Y0) => 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y3 = Y2)))))) => 236.86/34.89 (??(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (in(Y3, 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1)) & 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y1) = 236.86/34.89 setadjoin( 236.86/34.89 Y3, 236.86/34.89 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.89 inference('lazy_cnf_imply', [status(thm)], ['192'])). 236.86/34.89 tff('194', plain, 236.86/34.89 ~ ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (in(Y2, dsetconstr(Y0, Y1)) <=> Y1(Y2)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.89 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.89 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.89 (!!((^[Y3 : $o]: 236.86/34.89 (((Y2 = Y0) => Y3) => 236.86/34.89 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.89 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.89 in(Y1, powerset(Y0))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.89 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y1, powerset(Y0)) => 236.86/34.89 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y1, Y2) => 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 in(Y1, setunion(Y0))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, setunion(Y0)) => 236.86/34.89 (!!((^[Y2 : $o]: 236.86/34.89 ((!!((^[Y3 : $i]: 236.86/34.89 (in(Y1, Y3) => 236.86/34.89 (in(Y3, Y0) => Y2))))) => 236.86/34.89 Y2))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, Y0) => 236.86/34.89 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ((Y0 != emptyset) => 236.86/34.89 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.89 (Y0 = Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 != Y1) => 236.86/34.89 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.89 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, 236.86/34.89 emptyset))) => 236.86/34.89 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin(Y0, 236.86/34.89 setadjoin(Y1, emptyset))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.89 (dsetconstr(Y0, Y1) != 236.86/34.89 emptyset)))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2))))))) => 236.86/34.89 (~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2))))))) => 236.86/34.89 (~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $o]: 236.86/34.89 (Y0 => 236.86/34.89 in(emptyset, prop2set(Y0)))))) => 236.86/34.89 ((!!((^[Y0 : $o]: 236.86/34.89 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) => 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((~((!!((^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 Y1(Y2))))))) => 236.86/34.89 (??((^[Y2 : $i]: 236.86/34.89 (in(Y2, Y0) & 236.86/34.89 (~(Y1(Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??(Y0)) => 236.86/34.89 ((!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 (Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 (Y2 = Y1)))))))) => 236.86/34.89 (??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 ( 236.86/34.89 Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y3, 236.86/34.89 Y1)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) <=> 236.86/34.89 in(Y3, 236.86/34.89 Y1)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))) => 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!((^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 ((!!((^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 Y1(Y3))))))))) => 236.86/34.89 ((??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) & 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y0(Y3) => 236.86/34.89 (Y2 = Y3))))))))) <=> 236.86/34.89 (??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y1(Y2) & 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (setadjoin( 236.86/34.89 Y0, Y2) = 236.86/34.89 setadjoin( 236.86/34.89 Y1, Y3)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (powerset( 236.86/34.89 Y0) = 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ((Y0 = Y1) => 236.86/34.89 (setunion( 236.86/34.89 Y0) = 236.86/34.89 setunion( 236.86/34.89 Y1))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 ((??((^[Y1 : $i]: 236.86/34.89 (Y0(Y1) & 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))) => 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y1) => 236.86/34.89 (Y0(Y2) => 236.86/34.89 (Y1 = Y2))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i > $o]: 236.86/34.89 (!!((^[Y1 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (( 236.86/34.89 Y2 = Y3) => 236.86/34.89 (Y0(Y2) <=> 236.86/34.89 Y1(Y3))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y0(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y0(Y3) => 236.86/34.89 (Y2 = Y3))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (Y1(Y2) & 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i]: 236.86/34.89 (Y1(Y3) => 236.86/34.89 (Y2 = Y3))))))))) => 236.86/34.89 ( 236.86/34.89 descr(Y0) = 236.86/34.89 descr(Y1))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 Y0 = Y1) => 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i > $o]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $i > $o]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y4 : $i]: 236.86/34.89 (in(Y4, 236.86/34.89 Y0) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y5 : $i]: 236.86/34.89 (in(Y5, 236.86/34.89 Y1) => 236.86/34.89 (( 236.86/34.89 Y4 = Y5) => 236.86/34.89 (Y2(Y4) <=> 236.86/34.89 Y3(Y5))))))))))) => 236.86/34.89 (dsetconstr( 236.86/34.89 Y0, Y2) = 236.86/34.89 dsetconstr( 236.86/34.89 Y1, Y3)))))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!((^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 Y0 = Y1) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 Y0 = Y1) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ((!!(subset( 236.86/34.89 emptyset))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1)))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ((!!((^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 subset( 236.86/34.89 Y0, Y1))) => 236.86/34.89 (Y0 != Y1)))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (Y0 != Y1)))))))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, Y0)))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (subset( 236.86/34.89 Y1, Y2) => 236.86/34.89 subset( 236.86/34.89 Y0, Y2)))))))))))) => 236.86/34.89 ((!!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 (( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y2) => 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 in(Y0, 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 (Y0 = Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, 236.86/34.89 emptyset) => 236.86/34.89 (Y0 = 236.86/34.89 emptyset))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 in(Y1, 236.86/34.89 powerset( 236.86/34.89 Y0))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (in(Y1, 236.86/34.89 powerset( 236.86/34.89 Y0)) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 in(Y0, 236.86/34.89 powerset( 236.86/34.89 Y0))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 subset( 236.86/34.89 powerset( 236.86/34.89 Y0), 236.86/34.89 powerset( 236.86/34.89 Y1))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 in( 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1), 236.86/34.89 powerset( 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i > $o]: 236.86/34.89 subset( 236.86/34.89 dsetconstr( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 in(Y1, 236.86/34.89 setadjoin( 236.86/34.89 Y0, 236.86/34.89 setadjoin( 236.86/34.89 Y1, 236.86/34.89 emptyset))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $o]: 236.86/34.89 (in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => Y3) => 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y1) => Y3) => 236.86/34.89 Y3))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) | 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y0, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 Y1, 236.86/34.89 binunion( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y2, Y0) => 236.86/34.89 (subset( 236.86/34.89 Y2, Y1) => 236.86/34.89 subset( 236.86/34.89 Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y0))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y1) => 236.86/34.89 subset( 236.86/34.89 Y1, Y0)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 ~(( 236.86/34.89 ??(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) & 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 Y1))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y1, Y0) => 236.86/34.89 (binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1) = 236.86/34.89 Y0) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (binintersect( 236.86/34.89 Y0, 236.86/34.89 binunion( 236.86/34.89 Y1, Y2)) = 236.86/34.89 binunion( 236.86/34.89 binintersect( 236.86/34.89 Y0, Y1), 236.86/34.89 binintersect( 236.86/34.89 Y0, Y2)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 in(Y2, 236.86/34.89 Y0))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (subset( 236.86/34.89 Y0, Y1) => 236.86/34.89 (setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 in(Y2, 236.86/34.89 Y1)))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 Y0)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 setminus( 236.86/34.89 Y0, Y1)))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 subset( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1), 236.86/34.89 Y0))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (( 236.86/34.89 setminus( 236.86/34.89 Y0, Y1) = 236.86/34.89 emptyset) => 236.86/34.89 subset( 236.86/34.89 Y0, Y1)))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1)) => 236.86/34.89 (!!(( 236.86/34.89 ^[Y3 : $o]: 236.86/34.89 (( 236.86/34.89 in(Y2, 236.86/34.89 Y0) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 Y3)) => 236.86/34.89 (( 236.86/34.89 ( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 ( 236.86/34.89 in(Y2, 236.86/34.89 Y1) => Y3)) => 236.86/34.89 Y3))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y1))) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (( 236.86/34.89 ~( 236.86/34.89 in(Y2, 236.86/34.89 Y0))) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.89 (in(Y2, 236.86/34.89 Y0) => 236.86/34.89 (in(Y2, 236.86/34.89 Y1) => 236.86/34.89 (~( 236.86/34.89 in(Y2, 236.86/34.89 symdiff( 236.86/34.89 Y0, Y1))))))))))))))) => 236.86/34.89 ( 236.86/34.89 ( 236.86/34.89 !!(( 236.86/34.89 ^[Y0 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y1 : $i]: 236.86/34.89 (!!(( 236.86/34.89 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 Y0))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))) => 236.86/34.90 (( 236.86/34.90 Y2 = Y1) | 236.86/34.90 (Y2 = Y0)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) & 236.86/34.90 (??(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 Y1) & 236.86/34.90 (Y2 = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 setadjoin( 236.86/34.90 Y4, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 Y2)) & 236.86/34.90 (??(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 setunion( 236.86/34.90 Y2)) & 236.86/34.90 (Y2 = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 setadjoin( 236.86/34.90 Y4, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 setunion( 236.86/34.90 Y0)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 in(Y1, 236.86/34.90 Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)), 236.86/34.90 Y0)))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)) = 236.86/34.90 Y0)))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y2) => 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))))) => 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 Y1(Y2))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset)))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 Y1(Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y2) => 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y3 = Y2)))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.90 inference('lazy_cnf_imply', [status(thm)], ['193'])). 236.86/34.90 tff('195', plain, 236.86/34.90 ~ ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.90 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.90 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.90 (!!((^[Y3 : $o]: 236.86/34.90 (((Y2 = Y0) => Y3) => 236.86/34.90 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.90 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.90 in(Y1, powerset(Y0))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.90 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y1, powerset(Y0)) => 236.86/34.90 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y1, Y2) => 236.86/34.90 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, setunion(Y0)) => 236.86/34.90 (!!((^[Y2 : $o]: 236.86/34.90 ((!!((^[Y3 : $i]: 236.86/34.90 (in(Y1, Y3) => 236.86/34.90 (in(Y3, Y0) => Y2))))) => 236.86/34.90 Y2))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, Y0) => 236.86/34.90 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 ((Y0 != emptyset) => 236.86/34.90 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.90 (Y0 = Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 != Y1) => 236.86/34.90 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.90 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, 236.86/34.90 emptyset))) => 236.86/34.90 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.90 (dsetconstr(Y0, Y1) != 236.86/34.90 emptyset)))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2))))))) => 236.86/34.90 (~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2))))))) => 236.86/34.90 (~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $o]: 236.86/34.90 (Y0 => 236.86/34.90 in(emptyset, prop2set(Y0)))))) => 236.86/34.90 ((!!((^[Y0 : $o]: 236.86/34.90 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??(Y0)) => 236.86/34.90 ((!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y1) => 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 (Y2 = Y1)))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y3, 236.86/34.90 Y1)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) <=> 236.86/34.90 in(Y3, 236.86/34.90 Y1)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))) => 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 Y0(Y1) => 236.86/34.90 ( 236.86/34.90 Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 Y1(Y3))))))))) => 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y0(Y3) => 236.86/34.90 (Y2 = Y3))))))))) <=> 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (Y1(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (setadjoin( 236.86/34.90 Y0, Y2) = 236.86/34.90 setadjoin( 236.86/34.90 Y1, Y3)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (powerset(Y0) = 236.86/34.90 powerset(Y1))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (setunion( 236.86/34.90 Y0) = 236.86/34.90 setunion( 236.86/34.90 Y1))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))) => 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y0(Y1) => 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 Y1(Y3))))))))) => 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y0(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y0(Y3) => 236.86/34.90 (Y2 = Y3))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y1(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))) => 236.86/34.90 ( 236.86/34.90 descr(Y0) = 236.86/34.90 descr(Y1))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 Y0 = Y1) => 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i > $o]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i > $o]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y5 : $i]: 236.86/34.90 (in(Y5, 236.86/34.90 Y1) => 236.86/34.90 (( 236.86/34.90 Y4 = Y5) => 236.86/34.90 (Y2(Y4) <=> 236.86/34.90 Y3(Y5))))))))))) => 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y2) = 236.86/34.90 dsetconstr( 236.86/34.90 Y1, Y3)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 Y0 = Y1) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 Y0 = Y1) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!(subset( 236.86/34.90 emptyset))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 subset( 236.86/34.90 Y0, Y1))) => 236.86/34.90 (Y0 != Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (Y0 != Y1)))))))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, Y0)))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (subset( 236.86/34.90 Y1, Y2) => 236.86/34.90 subset( 236.86/34.90 Y0, Y2)))))))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y2) => 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, Y2)))))))))))) => 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 in(Y0, 236.86/34.90 powerset( 236.86/34.90 Y1))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 (Y0 = Y1))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, 236.86/34.90 emptyset) => 236.86/34.90 (Y0 = 236.86/34.90 emptyset))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 in(Y1, 236.86/34.90 powerset( 236.86/34.90 Y0))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 powerset( 236.86/34.90 Y0)) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 powerset( 236.86/34.90 Y0))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 subset( 236.86/34.90 powerset( 236.86/34.90 Y0), 236.86/34.90 powerset( 236.86/34.90 Y1))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 in( 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1), 236.86/34.90 powerset( 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 subset( 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $o]: 236.86/34.90 (in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => Y3) => 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y1) => Y3) => 236.86/34.90 Y3))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) | 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y1, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y2, Y0) => 236.86/34.90 (subset( 236.86/34.90 Y2, Y1) => 236.86/34.90 subset( 236.86/34.90 Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y0))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 ~(( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 Y1))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y0) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (binintersect( 236.86/34.90 Y0, 236.86/34.90 binunion( 236.86/34.90 Y1, Y2)) = 236.86/34.90 binunion( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 binintersect( 236.86/34.90 Y0, Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y0))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (setminus( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 setminus( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 setminus( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $o]: 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 Y3)) => 236.86/34.90 (( 236.86/34.90 ( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 ( 236.86/34.90 in(Y2, 236.86/34.90 Y1) => Y3)) => 236.86/34.90 Y3))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 Y0))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))) => 236.86/34.90 (( 236.86/34.90 Y2 = Y1) | 236.86/34.90 (Y2 = Y0)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) & 236.86/34.90 (??(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 Y1) & 236.86/34.90 (Y2 = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 setadjoin( 236.86/34.90 Y4, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 Y2)) & 236.86/34.90 (??(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 setunion( 236.86/34.90 Y2)) & 236.86/34.90 (Y2 = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 setadjoin( 236.86/34.90 Y4, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 setunion( 236.86/34.90 Y0)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 in(Y1, 236.86/34.90 Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)), 236.86/34.90 Y0)))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)) = 236.86/34.90 Y0)))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y2) => 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))))) => 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 Y1(Y2))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset)))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 Y1(Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y2) => 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y3 = Y2)))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.90 inference('lazy_cnf_imply', [status(thm)], ['194'])). 236.86/34.90 tff('196', plain, 236.86/34.90 ~ ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (Y1(Y2) => (dsetconstr(Y0, Y1) != emptyset)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.90 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.90 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.90 (!!((^[Y3 : $o]: 236.86/34.90 (((Y2 = Y0) => Y3) => 236.86/34.90 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.90 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.90 in(Y1, powerset(Y0))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.90 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y1, powerset(Y0)) => 236.86/34.90 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y1, Y2) => 236.86/34.90 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, setunion(Y0)) => 236.86/34.90 (!!((^[Y2 : $o]: 236.86/34.90 ((!!((^[Y3 : $i]: 236.86/34.90 (in(Y1, Y3) => 236.86/34.90 (in(Y3, Y0) => Y2))))) => 236.86/34.90 Y2))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, Y0) => 236.86/34.90 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 ((Y0 != emptyset) => 236.86/34.90 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.90 (Y0 = Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 != Y1) => 236.86/34.90 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.90 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))) => 236.86/34.90 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.90 (dsetconstr(Y0, Y1) != emptyset)))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2))))))) => 236.86/34.90 (~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2))))))) => 236.86/34.90 (~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $o]: 236.86/34.90 (Y0 => in(emptyset, prop2set(Y0)))))) => 236.86/34.90 ((!!((^[Y0 : $o]: 236.86/34.90 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??(Y0)) => 236.86/34.90 ((!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y1) => 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 (Y2 = Y1)))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 Y2 = Y3) => 236.86/34.90 ( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y3, 236.86/34.90 Y1)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) <=> 236.86/34.90 in(Y3, 236.86/34.90 Y1)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))) => 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y1) => 236.86/34.90 ( 236.86/34.90 Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!((^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 Y1(Y3))))))))) => 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y0(Y3) => 236.86/34.90 (Y2 = Y3))))))))) <=> 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (Y1(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (setadjoin( 236.86/34.90 Y0, Y2) = 236.86/34.90 setadjoin( 236.86/34.90 Y1, Y3)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (powerset(Y0) = 236.86/34.90 powerset(Y1))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (setunion(Y0) = 236.86/34.90 setunion(Y1))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))) => 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 Y0(Y1) => 236.86/34.90 ( 236.86/34.90 Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 Y1(Y3))))))))) => 236.86/34.90 ((??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y0(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y0(Y3) => 236.86/34.90 (Y2 = Y3))))))))) => 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y1(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))) => 236.86/34.90 ( 236.86/34.90 descr(Y0) = 236.86/34.90 descr(Y1))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i > $o]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i > $o]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y5 : $i]: 236.86/34.90 (in(Y5, 236.86/34.90 Y1) => 236.86/34.90 (( 236.86/34.90 Y4 = Y5) => 236.86/34.90 (Y2(Y4) <=> 236.86/34.90 Y3(Y5))))))))))) => 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y2) = 236.86/34.90 dsetconstr( 236.86/34.90 Y1, Y3)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 Y0 = Y1) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 Y0 = Y1) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!(subset(emptyset))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 subset( 236.86/34.90 Y0, Y1))) => 236.86/34.90 (Y0 != Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (Y0 != Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, Y0)))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (subset( 236.86/34.90 Y1, Y2) => 236.86/34.90 subset( 236.86/34.90 Y0, Y2)))))))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y2) => 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, Y2)))))))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 in(Y0, 236.86/34.90 powerset( 236.86/34.90 Y1))))))))) => 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 (Y0 = Y1))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, 236.86/34.90 emptyset) => 236.86/34.90 (Y0 = 236.86/34.90 emptyset))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 in(Y1, 236.86/34.90 powerset( 236.86/34.90 Y0))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 powerset( 236.86/34.90 Y0)) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 powerset( 236.86/34.90 Y0))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 subset( 236.86/34.90 powerset( 236.86/34.90 Y0), 236.86/34.90 powerset( 236.86/34.90 Y1))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 in( 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1), 236.86/34.90 powerset( 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 subset( 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $o]: 236.86/34.90 (in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => Y3) => 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y1) => Y3) => 236.86/34.90 Y3))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) | 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y1, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y2, Y0) => 236.86/34.90 (subset( 236.86/34.90 Y2, Y1) => 236.86/34.90 subset( 236.86/34.90 Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y0))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 ~(( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 Y1))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y0) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (binintersect( 236.86/34.90 Y0, 236.86/34.90 binunion( 236.86/34.90 Y1, Y2)) = 236.86/34.90 binunion( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 binintersect( 236.86/34.90 Y0, Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y0))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (setminus( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 setminus( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 setminus( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $o]: 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 Y3)) => 236.86/34.90 (( 236.86/34.90 ( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 ( 236.86/34.90 in(Y2, 236.86/34.90 Y1) => Y3)) => 236.86/34.90 Y3))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 Y0))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))) => 236.86/34.90 (( 236.86/34.90 Y2 = Y1) | 236.86/34.90 (Y2 = Y0)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) & 236.86/34.90 (??(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 Y1) & 236.86/34.90 (Y2 = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 setadjoin( 236.86/34.90 Y4, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 cartprod( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 Y2)) & 236.86/34.90 (??(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 setunion( 236.86/34.90 Y2)) & 236.86/34.90 (Y2 = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 setadjoin( 236.86/34.90 Y4, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 setunion( 236.86/34.90 Y0)) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 in(Y1, 236.86/34.90 Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)), 236.86/34.90 Y0)))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (setunion( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset)) = 236.86/34.90 Y0)))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y2) => 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))))) => 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 Y1(Y2))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset)))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 Y1(Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y2) => 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y0) => 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y3 = Y2)))))) => 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1)) & 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y1) = 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.90 inference('lazy_cnf_imply', [status(thm)], ['195'])). 236.86/34.90 tff('197', plain, 236.86/34.90 ~ ((!!((^[Y0 : $i]: ((??((^[Y1 : $i]: in(Y1, Y0)))) => (Y0 != emptyset))))) => 236.86/34.90 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.90 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.90 (!!((^[Y3 : $o]: 236.86/34.90 (((Y2 = Y0) => Y3) => 236.86/34.90 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.90 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.90 in(Y1, powerset(Y0))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.90 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y1, powerset(Y0)) => 236.86/34.90 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y1, Y2) => 236.86/34.90 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, setunion(Y0)) => 236.86/34.90 (!!((^[Y2 : $o]: 236.86/34.90 ((!!((^[Y3 : $i]: 236.86/34.90 (in(Y1, Y3) => 236.86/34.90 (in(Y3, Y0) => Y2))))) => 236.86/34.90 Y2))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, Y0) => 236.86/34.90 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 ((Y0 != emptyset) => 236.86/34.90 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.90 (Y0 = Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 != Y1) => 236.86/34.90 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.90 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))) => 236.86/34.90 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin(Y0, 236.86/34.90 setadjoin(Y1, emptyset))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.90 (dsetconstr(Y0, Y1) != emptyset)))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2))))))) => 236.86/34.90 (~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2))))))) => 236.86/34.90 (~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $o]: 236.86/34.90 (Y0 => in(emptyset, prop2set(Y0)))))) => 236.86/34.90 ((!!((^[Y0 : $o]: 236.86/34.90 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((~((!!((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) => 236.86/34.90 Y1(Y2))))))) => 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 (in(Y2, Y0) & 236.86/34.90 (~(Y1(Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??(Y0)) => 236.86/34.90 ((!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y1) => 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 (Y2 = Y1)))))))) => 236.86/34.90 (??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 (Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 ( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y3, 236.86/34.90 Y1)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 Y2 = Y3) => 236.86/34.90 ( 236.86/34.90 in(Y2, 236.86/34.90 Y0) <=> 236.86/34.90 in(Y3, 236.86/34.90 Y1)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))) => 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 (Y0(Y1) => 236.86/34.90 (Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!((^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 Y1(Y3))))))))) => 236.86/34.90 ((??((^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 Y0(Y2) & 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y0(Y3) => 236.86/34.90 (Y2 = Y3))))))))) <=> 236.86/34.90 (??((^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 Y1(Y2) & 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!((^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (setadjoin( 236.86/34.90 Y0, Y2) = 236.86/34.90 setadjoin( 236.86/34.90 Y1, Y3)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (powerset(Y0) = 236.86/34.90 powerset(Y1))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (setunion(Y0) = 236.86/34.90 setunion(Y1))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 ((??((^[Y1 : $i]: 236.86/34.90 (Y0(Y1) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))) => 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y0(Y1) => 236.86/34.90 ( 236.86/34.90 Y0(Y2) => 236.86/34.90 ( 236.86/34.90 Y1 = Y2))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i > $o]: 236.86/34.90 (!!((^[Y1 : $i > $o]: 236.86/34.90 ((!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (( 236.86/34.90 Y2 = Y3) => 236.86/34.90 (Y0(Y2) <=> 236.86/34.90 Y1(Y3))))))))) => 236.86/34.90 ((??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y0(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y0(Y3) => 236.86/34.90 (Y2 = Y3))))))))) => 236.86/34.90 ((??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (Y1(Y2) & 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (Y1(Y3) => 236.86/34.90 (Y2 = Y3))))))))) => 236.86/34.90 (descr(Y0) = 236.86/34.90 descr(Y1))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((Y0 = Y1) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i > $o]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i > $o]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y4 : $i]: 236.86/34.90 (in(Y4, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y5 : $i]: 236.86/34.90 (in(Y5, 236.86/34.90 Y1) => 236.86/34.90 (( 236.86/34.90 Y4 = Y5) => 236.86/34.90 (Y2(Y4) <=> 236.86/34.90 Y3(Y5))))))))))) => 236.86/34.90 (dsetconstr( 236.86/34.90 Y0, Y2) = 236.86/34.90 dsetconstr( 236.86/34.90 Y1, Y3)))))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ((!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 Y0 = Y1) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 Y0 = Y1) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!((^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!(subset(emptyset))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 subset( 236.86/34.90 Y0, Y1))) => 236.86/34.90 (Y0 != Y1)))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (Y0 != Y1)))))))))))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, Y0)))) => 236.86/34.90 ((!!((^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (subset( 236.86/34.90 Y1, Y2) => 236.86/34.90 subset( 236.86/34.90 Y0, Y2)))))))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y2) => 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, Y2)))))))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 in(Y0, 236.86/34.90 powerset( 236.86/34.90 Y1))))))))) => 236.86/34.90 ((!!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 (Y0 = Y1))))))))) => 236.86/34.90 (( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, 236.86/34.90 emptyset) => 236.86/34.90 (Y0 = 236.86/34.90 emptyset))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 in(Y1, 236.86/34.90 powerset( 236.86/34.90 Y0))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 powerset( 236.86/34.90 Y0)) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 powerset( 236.86/34.90 Y0))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 subset( 236.86/34.90 powerset( 236.86/34.90 Y0), 236.86/34.90 powerset( 236.86/34.90 Y1))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 in( 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1), 236.86/34.90 powerset( 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i > $o]: 236.86/34.90 subset( 236.86/34.90 dsetconstr( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $o]: 236.86/34.90 (in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => Y3) => 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y1) => Y3) => 236.86/34.90 Y3))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) | 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y0, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 Y1, 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y2, Y0) => 236.86/34.90 (subset( 236.86/34.90 Y2, Y1) => 236.86/34.90 subset( 236.86/34.90 Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y0))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 Y1, Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 ~(( 236.86/34.90 ??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) & 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 Y1))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y1, Y0) => 236.86/34.90 (binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1) = 236.86/34.90 Y0) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (binintersect( 236.86/34.90 Y0, 236.86/34.90 binunion( 236.86/34.90 Y1, Y2)) = 236.86/34.90 binunion( 236.86/34.90 binintersect( 236.86/34.90 Y0, Y1), 236.86/34.90 binintersect( 236.86/34.90 Y0, Y2)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)) => 236.86/34.90 in(Y2, 236.86/34.90 Y0))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (subset( 236.86/34.90 Y0, Y1) => 236.86/34.90 (setminus( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))) => 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in(Y2, 236.86/34.90 Y1)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 Y0)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 setminus( 236.86/34.90 Y0, Y1)))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 subset( 236.86/34.90 setminus( 236.86/34.90 Y0, Y1), 236.86/34.90 Y0))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (( 236.86/34.90 setminus( 236.86/34.90 Y0, Y1) = 236.86/34.90 emptyset) => 236.86/34.90 subset( 236.86/34.90 Y0, Y1)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1)) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $o]: 236.86/34.90 (( 236.86/34.90 in(Y2, 236.86/34.90 Y0) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 Y3)) => 236.86/34.90 (( 236.86/34.90 ( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 ( 236.86/34.90 in(Y2, 236.86/34.90 Y1) => Y3)) => 236.86/34.90 Y3))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (in(Y2, 236.86/34.90 Y1) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y0))) => 236.86/34.90 (( 236.86/34.90 ~( 236.86/34.90 in(Y2, 236.86/34.90 Y1))) => 236.86/34.90 (~( 236.86/34.90 in(Y2, 236.86/34.90 symdiff( 236.86/34.90 Y0, Y1))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y0, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 in(Y1, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (??(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (??(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 setunion( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)))) & 236.86/34.90 (setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)) = 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 Y0)))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (in(Y1, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 Y0))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y0, 236.86/34.90 setadjoin( 236.86/34.90 Y1, 236.86/34.90 emptyset))) => 236.86/34.90 (( 236.86/34.90 Y2 = Y1) | 236.86/34.90 (Y2 = Y0)))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 subset( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 setadjoin( 236.86/34.90 Y3, 236.86/34.90 emptyset)), 236.86/34.90 emptyset)), 236.86/34.90 powerset( 236.86/34.90 powerset( 236.86/34.90 binunion( 236.86/34.90 Y0, Y1)))))))))))))))))) => 236.86/34.90 ( 236.86/34.90 ( 236.86/34.90 !!(( 236.86/34.90 ^[Y0 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y1 : $i]: 236.86/34.90 (!!(( 236.86/34.90 ^[Y2 : $i]: 236.86/34.90 (in(Y2, 236.86/34.90 Y0) => 236.86/34.90 (!!(( 236.86/34.90 ^[Y3 : $i]: 236.86/34.90 (in(Y3, 236.86/34.90 Y1) => 236.86/34.90 in( 236.86/34.90 setadjoin( 236.86/34.90 setadjoin( 236.86/34.90 Y2, 236.86/34.90 emptyset), 236.86/34.90 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 Y1) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 setunion( 236.86/34.91 Y0)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 in(Y1, 236.86/34.91 Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)), 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)) = 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))))) => 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y3 = Y2)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.91 inference('lazy_cnf_imply', [status(thm)], ['196'])). 236.86/34.91 tff('198', plain, 236.86/34.91 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, Y1)))))))) => 236.86/34.91 (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (!!((^[Y3 : $o]: 236.86/34.91 (((Y2 = Y0) => Y3) => 236.86/34.91 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.91 in(Y1, powerset(Y0))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, powerset(Y0)) => 236.86/34.91 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, Y2) => 236.86/34.91 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, setunion(Y0)) => 236.86/34.91 (!!((^[Y2 : $o]: 236.86/34.91 ((!!((^[Y3 : $i]: 236.86/34.91 (in(Y1, Y3) => 236.86/34.91 (in(Y3, Y0) => Y2))))) => 236.86/34.91 Y2))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, Y0) => 236.86/34.91 in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 ((Y0 != emptyset) => 236.86/34.91 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 (Y0 = Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 != Y1) => 236.86/34.91 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))) => 236.86/34.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2))))))) => 236.86/34.91 (~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2))))))) => 236.86/34.91 (~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => in(emptyset, prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??(Y0)) => 236.86/34.91 ((!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 (Y2 = Y1)))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y0) <=> 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) & 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y0(Y3) => 236.86/34.91 (Y2 = Y3))))))))) <=> 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (Y1(Y2) & 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (setadjoin( 236.86/34.91 Y0, Y2) = 236.86/34.91 setadjoin( 236.86/34.91 Y1, Y3)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (powerset(Y0) = 236.86/34.91 powerset(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (setunion(Y0) = 236.86/34.91 setunion(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 ( 236.86/34.91 Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 ( 236.86/34.91 Y0(Y2) & 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y0(Y3) => 236.86/34.91 (Y2 = Y3))))))))) => 236.86/34.91 ((??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (Y1(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))) => 236.86/34.91 (descr(Y0) = 236.86/34.91 descr(Y1))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i > $o]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i > $o]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y5 : $i]: 236.86/34.91 (in(Y5, 236.86/34.91 Y1) => 236.86/34.91 (( 236.86/34.91 Y4 = Y5) => 236.86/34.91 (Y2(Y4) <=> 236.86/34.91 Y3(Y5))))))))))) => 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y2) = 236.86/34.91 dsetconstr( 236.86/34.91 Y1, Y3)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))) => 236.86/34.91 subset(Y0, 236.86/34.91 Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 subset( 236.86/34.91 Y1, Y0)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 Y0 = Y1) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!(subset(emptyset))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 subset( 236.86/34.91 Y0, Y1))) => 236.86/34.91 (Y0 != Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (Y0 != Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, Y0)))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (subset( 236.86/34.91 Y1, Y2) => 236.86/34.91 subset( 236.86/34.91 Y0, Y2)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y2) => 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, Y2)))))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 in(Y0, 236.86/34.91 powerset( 236.86/34.91 Y1))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 (Y0 = Y1))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, 236.86/34.91 emptyset) => 236.86/34.91 (Y0 = 236.86/34.91 emptyset))))) => 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 in(Y1, 236.86/34.91 powerset( 236.86/34.91 Y0))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 powerset( 236.86/34.91 Y0)) => 236.86/34.91 subset( 236.86/34.91 Y1, Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 powerset( 236.86/34.91 Y0))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 subset( 236.86/34.91 powerset( 236.86/34.91 Y0), 236.86/34.91 powerset( 236.86/34.91 Y1))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 in( 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1), 236.86/34.91 powerset( 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 subset( 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $o]: 236.86/34.91 (in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => Y3) => 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y1) => Y3) => 236.86/34.91 Y3))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) | 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y1, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y2, Y0) => 236.86/34.91 (subset( 236.86/34.91 Y2, Y1) => 236.86/34.91 subset( 236.86/34.91 Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y0))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 Y1, Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 ~(( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 Y1))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y0) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (binintersect( 236.86/34.91 Y0, 236.86/34.91 binunion( 236.86/34.91 Y1, Y2)) = 236.86/34.91 binunion( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 binintersect( 236.86/34.91 Y0, Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y0))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (setminus( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 setminus( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 setminus( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $o]: 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 Y3)) => 236.86/34.91 (( 236.86/34.91 ( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y1) => Y3)) => 236.86/34.91 Y3))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)) = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)) = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 Y0) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset), 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 Y0) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset), 236.86/34.91 powerset( 236.86/34.91 Y0))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))) => 236.86/34.91 (( 236.86/34.91 Y2 = Y1) | 236.86/34.91 (Y2 = Y0)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 Y1) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 setunion( 236.86/34.91 Y0)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 in(Y1, 236.86/34.91 Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)), 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)) = 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))))) => 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y3 = Y2)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.91 inference('lazy_cnf_imply', [status(thm)], ['197'])). 236.86/34.91 tff('199', plain, 236.86/34.91 ~ (in(emptyset, setadjoin(emptyset, emptyset)) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (!!((^[Y3 : $o]: 236.86/34.91 (((Y2 = Y0) => Y3) => 236.86/34.91 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.91 in(Y1, powerset(Y0))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, powerset(Y0)) => 236.86/34.91 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, Y2) => 236.86/34.91 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, setunion(Y0)) => 236.86/34.91 (!!((^[Y2 : $o]: 236.86/34.91 ((!!((^[Y3 : $i]: 236.86/34.91 (in(Y1, Y3) => 236.86/34.91 (in(Y3, Y0) => Y2))))) => 236.86/34.91 Y2))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 ((Y0 != emptyset) => 236.86/34.91 (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 (Y0 = Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 != Y1) => 236.86/34.91 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))) => 236.86/34.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2))))))) => 236.86/34.91 (~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2))))))) => 236.86/34.91 (~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => in(emptyset, prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??(Y0)) => 236.86/34.91 ((!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 (Y2 = Y1)))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) <=> 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y0(Y3) => 236.86/34.91 (Y2 = Y3))))))))) <=> 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (Y1(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (setadjoin( 236.86/34.91 Y0, Y2) = 236.86/34.91 setadjoin( 236.86/34.91 Y1, Y3)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (powerset(Y0) = 236.86/34.91 powerset(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (setunion(Y0) = 236.86/34.91 setunion(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (Y0(Y2) & 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y0(Y3) => 236.86/34.91 (Y2 = Y3))))))))) => 236.86/34.91 ((??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 ( 236.86/34.91 Y1(Y2) & 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))) => 236.86/34.91 (descr(Y0) = 236.86/34.91 descr(Y1))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i > $o]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i > $o]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y5 : $i]: 236.86/34.91 (in(Y5, 236.86/34.91 Y1) => 236.86/34.91 (( 236.86/34.91 Y4 = Y5) => 236.86/34.91 (Y2(Y4) <=> 236.86/34.91 Y3(Y5))))))))))) => 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y2) = 236.86/34.91 dsetconstr( 236.86/34.91 Y1, Y3)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))) => 236.86/34.91 subset(Y0, 236.86/34.91 Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 subset(Y1, 236.86/34.91 Y0)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!(subset(emptyset))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 ~( 236.86/34.91 subset( 236.86/34.91 Y0, Y1))) => 236.86/34.91 ( 236.86/34.91 Y0 != Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (Y0 != Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, Y0)))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (subset( 236.86/34.91 Y1, Y2) => 236.86/34.91 subset( 236.86/34.91 Y0, Y2)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y2) => 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, Y2)))))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 in(Y0, 236.86/34.91 powerset( 236.86/34.91 Y1))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 (Y0 = Y1))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, 236.86/34.91 emptyset) => 236.86/34.91 (Y0 = 236.86/34.91 emptyset))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 in(Y1, 236.86/34.91 powerset( 236.86/34.91 Y0))))))))) => 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 powerset( 236.86/34.91 Y0)) => 236.86/34.91 subset( 236.86/34.91 Y1, Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 powerset( 236.86/34.91 Y0))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 subset( 236.86/34.91 powerset( 236.86/34.91 Y0), 236.86/34.91 powerset( 236.86/34.91 Y1))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 in( 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1), 236.86/34.91 powerset( 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 subset( 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $o]: 236.86/34.91 (in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => Y3) => 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y1) => Y3) => 236.86/34.91 Y3))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) | 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y1, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y2, Y0) => 236.86/34.91 (subset( 236.86/34.91 Y2, Y1) => 236.86/34.91 subset( 236.86/34.91 Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y0))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 Y1, Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 ~(( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 Y1))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y0) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (binintersect( 236.86/34.91 Y0, 236.86/34.91 binunion( 236.86/34.91 Y1, Y2)) = 236.86/34.91 binunion( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 binintersect( 236.86/34.91 Y0, Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y0))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (setminus( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 setminus( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 setminus( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $o]: 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 Y3)) => 236.86/34.91 (( 236.86/34.91 ( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y1) => Y3)) => 236.86/34.91 Y3))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)) = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)) = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 Y0) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset), 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 Y0) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset), 236.86/34.91 powerset( 236.86/34.91 Y0))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))) => 236.86/34.91 (( 236.86/34.91 Y2 = Y1) | 236.86/34.91 (Y2 = Y0)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 Y1) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 setunion( 236.86/34.91 Y0)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 in(Y1, 236.86/34.91 Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)), 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)) = 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))))) => 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y3 = Y2)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.91 inference('lazy_cnf_imply', [status(thm)], ['198'])). 236.86/34.91 tff('200', plain, 236.86/34.91 ~ ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y1) => in(Y2, setadjoin(Y0, Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (!!((^[Y3 : $o]: 236.86/34.91 (((Y2 = Y0) => Y3) => 236.86/34.91 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.91 in(Y1, powerset(Y0))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, powerset(Y0)) => 236.86/34.91 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, Y2) => 236.86/34.91 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, setunion(Y0)) => 236.86/34.91 (!!((^[Y2 : $o]: 236.86/34.91 ((!!((^[Y3 : $i]: 236.86/34.91 (in(Y1, Y3) => 236.86/34.91 (in(Y3, Y0) => Y2))))) => 236.86/34.91 Y2))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 (Y0 = Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 != Y1) => 236.86/34.91 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))) => 236.86/34.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2))))))) => 236.86/34.91 (~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2))))))) => 236.86/34.91 (~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => in(emptyset, prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??(Y0)) => 236.86/34.91 ((!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 (Y2 = Y1)))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) <=> 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y0(Y3) => 236.86/34.91 (Y2 = Y3))))))))) <=> 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (Y1(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 setadjoin( 236.86/34.91 Y0, Y2) = 236.86/34.91 setadjoin( 236.86/34.91 Y1, Y3)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (powerset(Y0) = 236.86/34.91 powerset(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (setunion(Y0) = 236.86/34.91 setunion(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 ( 236.86/34.91 Y0(Y1) => 236.86/34.91 ( 236.86/34.91 Y0(Y2) => 236.86/34.91 ( 236.86/34.91 Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y0(Y3) => 236.86/34.91 (Y2 = Y3))))))))) => 236.86/34.91 ((??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (Y1(Y2) & 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))) => 236.86/34.91 (descr(Y0) = 236.86/34.91 descr(Y1))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i > $o]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i > $o]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y5 : $i]: 236.86/34.91 (in(Y5, 236.86/34.91 Y1) => 236.86/34.91 (( 236.86/34.91 Y4 = Y5) => 236.86/34.91 (Y2(Y4) <=> 236.86/34.91 Y3(Y5))))))))))) => 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y2) = 236.86/34.91 dsetconstr( 236.86/34.91 Y1, Y3)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))) => 236.86/34.91 subset(Y0, 236.86/34.91 Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 subset(Y1, 236.86/34.91 Y0)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 subset(Y0, 236.86/34.91 Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!(subset(emptyset))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 subset( 236.86/34.91 Y0, Y1))) => 236.86/34.91 ( 236.86/34.91 Y0 != Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (Y0 != Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 subset(Y0, 236.86/34.91 Y0)))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (subset( 236.86/34.91 Y1, Y2) => 236.86/34.91 subset( 236.86/34.91 Y0, Y2)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y2) => 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, Y2)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 in(Y0, 236.86/34.91 powerset( 236.86/34.91 Y1))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 (Y0 = Y1))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 ( 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 emptyset) => 236.86/34.91 ( 236.86/34.91 Y0 = 236.86/34.91 emptyset))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 in(Y1, 236.86/34.91 powerset( 236.86/34.91 Y0))))))))) => 236.86/34.91 ((!!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 powerset( 236.86/34.91 Y0)) => 236.86/34.91 subset( 236.86/34.91 Y1, Y0)))))))) => 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 powerset( 236.86/34.91 Y0))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 subset( 236.86/34.91 powerset( 236.86/34.91 Y0), 236.86/34.91 powerset( 236.86/34.91 Y1))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 in( 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1), 236.86/34.91 powerset( 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 subset( 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $o]: 236.86/34.91 (in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => Y3) => 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y1) => Y3) => 236.86/34.91 Y3))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) | 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 Y1, 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y2, Y0) => 236.86/34.91 (subset( 236.86/34.91 Y2, Y1) => 236.86/34.91 subset( 236.86/34.91 Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y0))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 Y1, Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 ~(( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 Y1))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y1, Y0) => 236.86/34.91 (binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1) = 236.86/34.91 Y0) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (binintersect( 236.86/34.91 Y0, 236.86/34.91 binunion( 236.86/34.91 Y1, Y2)) = 236.86/34.91 binunion( 236.86/34.91 binintersect( 236.86/34.91 Y0, Y1), 236.86/34.91 binintersect( 236.86/34.91 Y0, Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)) => 236.86/34.91 in(Y2, 236.86/34.91 Y0))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (subset( 236.86/34.91 Y0, Y1) => 236.86/34.91 (setminus( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))) => 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y2, 236.86/34.91 Y1)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 Y0)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 setminus( 236.86/34.91 Y0, Y1)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 subset( 236.86/34.91 setminus( 236.86/34.91 Y0, Y1), 236.86/34.91 Y0))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (( 236.86/34.91 setminus( 236.86/34.91 Y0, Y1) = 236.86/34.91 emptyset) => 236.86/34.91 subset( 236.86/34.91 Y0, Y1)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $o]: 236.86/34.91 (( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 Y3)) => 236.86/34.91 (( 236.86/34.91 ( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y1) => Y3)) => 236.86/34.91 Y3))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (in(Y2, 236.86/34.91 Y1) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y0))) => 236.86/34.91 (( 236.86/34.91 ~( 236.86/34.91 in(Y2, 236.86/34.91 Y1))) => 236.86/34.91 (~( 236.86/34.91 in(Y2, 236.86/34.91 symdiff( 236.86/34.91 Y0, Y1))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)) = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)))) & 236.86/34.91 (setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)) = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 Y0) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset), 236.86/34.91 Y0)))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 Y0) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset), 236.86/34.91 powerset( 236.86/34.91 Y0))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 setadjoin( 236.86/34.91 Y1, 236.86/34.91 emptyset))) => 236.86/34.91 (( 236.86/34.91 Y2 = Y1) | 236.86/34.91 (Y2 = Y0)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 subset( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 powerset( 236.86/34.91 powerset( 236.86/34.91 binunion( 236.86/34.91 Y0, Y1)))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y1) => 236.86/34.91 in( 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)), 236.86/34.91 emptyset)), 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 Y1) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 cartprod( 236.86/34.91 Y0, Y1)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (??(( 236.86/34.91 ^[Y4 : $i]: 236.86/34.91 (in(Y4, 236.86/34.91 setunion( 236.86/34.91 Y2)) & 236.86/34.91 (Y2 = 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset), 236.86/34.91 setadjoin( 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 setadjoin( 236.86/34.91 Y4, 236.86/34.91 emptyset)), 236.86/34.91 emptyset))))))))))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i]: 236.86/34.91 (in(Y1, 236.86/34.91 setunion( 236.86/34.91 Y0)) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 in(Y1, 236.86/34.91 Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)), 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 subset( 236.86/34.91 Y0, 236.86/34.91 setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (setunion( 236.86/34.91 setadjoin( 236.86/34.91 Y0, 236.86/34.91 emptyset)) = 236.86/34.91 Y0)))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y2 = Y3))))))))))) => 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))))))))))) => 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (( 236.86/34.91 ??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y2, 236.86/34.91 emptyset)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) & 236.86/34.91 Y1(Y2)))))))))))) => 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y0 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y1 : $i > $o]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y2) => 236.86/34.91 (( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 Y0) => 236.86/34.91 (Y1(Y3) => 236.86/34.91 (Y3 = Y2)))))) => 236.86/34.91 (??(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (in(Y3, 236.86/34.91 dsetconstr( 236.86/34.91 Y0, Y1)) & 236.86/34.91 (dsetconstr( 236.86/34.91 Y0, Y1) = 236.86/34.91 setadjoin( 236.86/34.91 Y3, 236.86/34.91 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 236.86/34.91 inference('lazy_cnf_imply', [status(thm)], ['199'])). 236.86/34.91 tff('201', plain, 236.86/34.91 ~ ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (!!((^[Y3 : $o]: 236.86/34.91 (((Y2 = Y0) => Y3) => 236.86/34.91 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, setadjoin(Y0, Y1)) => 236.86/34.91 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 236.86/34.91 in(Y1, powerset(Y0))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, powerset(Y0)) => 236.86/34.91 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y1, Y2) => 236.86/34.91 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, setunion(Y0)) => 236.86/34.91 (!!((^[Y2 : $o]: 236.86/34.91 ((!!((^[Y3 : $i]: 236.86/34.91 (in(Y1, Y3) => 236.86/34.91 (in(Y3, Y0) => Y2))))) => 236.86/34.91 Y2))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 (Y0 = Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 != Y1) => 236.86/34.91 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 in(Y0, setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y0, setadjoin(Y1, emptyset)) => 236.86/34.91 in(Y1, setadjoin(Y0, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))) => 236.86/34.91 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y0, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 in(Y1, 236.86/34.91 setadjoin(Y0, 236.86/34.91 setadjoin(Y1, emptyset))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2))))) => 236.86/34.91 (dsetconstr(Y0, Y1) != emptyset)))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (in(Y1, emptyset) => Y0(Y1)))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => (~(Y1(Y2))))))) => 236.86/34.91 (~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2))))))) => 236.86/34.91 (~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => in(emptyset, prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $o]: 236.86/34.91 (Y0 => set2prop(prop2set(Y0)))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((~((!!((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) => 236.86/34.91 Y1(Y2))))))) => 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (in(Y2, Y0) & 236.86/34.91 (~(Y1(Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??(Y0)) => 236.86/34.91 ((!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2)))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 (Y2 = Y1)))))))) => 236.86/34.91 (??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y0) => 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 ( 236.86/34.91 ( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 in(Y2, 236.86/34.91 Y0) <=> 236.86/34.91 in(Y3, 236.86/34.91 Y1)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 (Y0(Y2) => 236.86/34.91 (Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 (!!((^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 ( 236.86/34.91 Y0(Y3) => 236.86/34.91 ( 236.86/34.91 Y2 = Y3))))))))) <=> 236.86/34.91 (??((^[Y2 : $i]: 236.86/34.91 (Y1(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 ( 236.86/34.91 Y1(Y3) => 236.86/34.91 ( 236.86/34.91 Y2 = Y3))))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 ( 236.86/34.91 setadjoin( 236.86/34.91 Y0, Y2) = 236.86/34.91 setadjoin( 236.86/34.91 Y1, Y3)))))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (powerset(Y0) = 236.86/34.91 powerset(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i]: 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 ((Y0 = Y1) => 236.86/34.91 (setunion(Y0) = 236.86/34.91 setunion(Y1))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 ((??((^[Y1 : $i]: 236.86/34.91 (Y0(Y1) & 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 ( 236.86/34.91 Y0(Y2) => 236.86/34.91 ( 236.86/34.91 Y1 = Y2))))))))) => 236.86/34.91 (!!((^[Y1 : $i]: 236.86/34.91 (!!((^[Y2 : $i]: 236.86/34.91 (Y0(Y1) => 236.86/34.91 ( 236.86/34.91 Y0(Y2) => 236.86/34.91 ( 236.86/34.91 Y1 = Y2))))))))))))) => 236.86/34.91 ((!!((^[Y0 : $i > $o]: 236.86/34.91 (!!((^[Y1 : $i > $o]: 236.86/34.91 ((!!((^[Y2 : $i]: 236.86/34.91 ( 236.86/34.91 !!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.91 (( 236.86/34.91 Y2 = Y3) => 236.86/34.91 (Y0(Y2) <=> 236.86/34.91 Y1(Y3))))))))) => 236.86/34.91 ((??((^[Y2 : $i]: 236.86/34.91 (Y0(Y2) & 236.86/34.91 (!!(( 236.86/34.91 ^[Y3 : $i]: 236.86/34.92 (Y0(Y3) => 236.86/34.92 (Y2 = Y3))))))))) => 236.86/34.92 ((??((^[Y2 : $i]: 236.86/34.92 (Y1(Y2) & 236.86/34.92 (!!(( 236.86/34.92 ^[Y3 : $i]: 236.86/34.92 (Y1(Y3) => 236.86/34.92 (Y2 = Y3))))))))) => 236.86/34.92 (descr(Y0) = 236.86/34.92 descr(Y1))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 ((Y0 = Y1) => 236.86/34.92 (!!((^[Y2 : $i > $o]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y3 : $i > $o]: 236.86/34.92 (( 236.86/34.92 !!(( 236.86/34.92 ^[Y4 : $i]: 236.86/34.92 (in(Y4, 236.86/34.92 Y0) => 236.86/34.92 (!!(( 236.86/34.92 ^[Y5 : $i]: 236.86/34.92 (in(Y5, 236.86/34.92 Y1) => 236.86/34.92 (( 236.86/34.92 Y4 = Y5) => 236.86/34.92 (Y2(Y4) <=> 236.86/34.92 Y3(Y5))))))))))) => 236.86/34.92 (dsetconstr( 236.86/34.92 Y0, Y2) = 236.86/34.92 dsetconstr( 236.86/34.92 Y1, Y3)))))))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 ((!!((^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 in(Y2, 236.86/34.92 Y1))))) => 236.86/34.92 subset(Y0, Y1)))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 ((Y0 = Y1) => 236.86/34.92 subset(Y1, 236.86/34.92 Y0)))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 ((Y0 = Y1) => 236.86/34.92 subset(Y0, 236.86/34.92 Y1)))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 ((!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 in(Y2, 236.86/34.92 Y1))))) => 236.86/34.92 subset(Y0, 236.86/34.92 Y1)))))))) => 236.86/34.92 ((!!(subset(emptyset))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 in(Y2, 236.86/34.92 Y1)))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 (~( 236.86/34.92 in(Y2, 236.86/34.92 Y0)))))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 (~( 236.86/34.92 subset( 236.86/34.92 Y0, Y1)))))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!((^[Y1 : $i]: 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 subset( 236.86/34.92 Y0, Y1))) => 236.86/34.92 (Y0 != Y1)))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 (Y0 != Y1)))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 subset(Y0, 236.86/34.92 Y0)))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 (subset( 236.86/34.92 Y1, Y2) => 236.86/34.92 subset( 236.86/34.92 Y0, Y2)))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 subset( 236.86/34.92 Y1, 236.86/34.92 setadjoin( 236.86/34.92 Y0, Y1)))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y2) => 236.86/34.92 subset( 236.86/34.92 Y0, 236.86/34.92 setadjoin( 236.86/34.92 Y1, Y2)))))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 in(Y0, 236.86/34.92 powerset( 236.86/34.92 Y1))))))))) => 236.86/34.92 ((!!((^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 (subset( 236.86/34.92 Y1, Y0) => 236.86/34.92 (Y0 = Y1))))))))) => 236.86/34.92 ((!!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, 236.86/34.92 emptyset) => 236.86/34.92 ( 236.86/34.92 Y0 = 236.86/34.92 emptyset))))) => 236.86/34.92 ((!!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y1, Y0) => 236.86/34.92 in(Y1, 236.86/34.92 powerset( 236.86/34.92 Y0))))))))) => 236.86/34.92 ((!!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (in(Y1, 236.86/34.92 powerset( 236.86/34.92 Y0)) => 236.86/34.92 subset( 236.86/34.92 Y1, Y0)))))))) => 236.86/34.92 ((!!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 in(Y0, 236.86/34.92 powerset( 236.86/34.92 Y0))))) => 236.86/34.92 (( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 subset( 236.86/34.92 powerset( 236.86/34.92 Y0), 236.86/34.92 powerset( 236.86/34.92 Y1))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i > $o]: 236.86/34.92 in( 236.86/34.92 dsetconstr( 236.86/34.92 Y0, Y1), 236.86/34.92 powerset( 236.86/34.92 Y0)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i > $o]: 236.86/34.92 subset( 236.86/34.92 dsetconstr( 236.86/34.92 Y0, Y1), 236.86/34.92 Y0))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 in(Y2, 236.86/34.92 binunion( 236.86/34.92 Y0, Y1)))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 in(Y1, 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 setadjoin( 236.86/34.92 Y1, 236.86/34.92 emptyset))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y1) => 236.86/34.92 in(Y2, 236.86/34.92 binunion( 236.86/34.92 Y0, Y1)))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y3 : $o]: 236.86/34.92 (in(Y2, 236.86/34.92 binunion( 236.86/34.92 Y0, Y1)) => 236.86/34.92 (( 236.86/34.92 in(Y2, 236.86/34.92 Y0) => Y3) => 236.86/34.92 (( 236.86/34.92 in(Y2, 236.86/34.92 Y1) => Y3) => 236.86/34.92 Y3))))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 binunion( 236.86/34.92 Y0, Y1)) => 236.86/34.92 (in(Y2, 236.86/34.92 Y1) | 236.86/34.92 in(Y2, 236.86/34.92 Y0)))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 subset( 236.86/34.92 Y0, 236.86/34.92 binunion( 236.86/34.92 Y0, Y1)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 subset( 236.86/34.92 Y1, 236.86/34.92 binunion( 236.86/34.92 Y0, Y1)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 (in(Y2, 236.86/34.92 Y1) => 236.86/34.92 in(Y2, 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y2, Y0) => 236.86/34.92 (subset( 236.86/34.92 Y2, Y1) => 236.86/34.92 subset( 236.86/34.92 Y2, 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1)) => 236.86/34.92 in(Y2, 236.86/34.92 Y0))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 subset( 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1), 236.86/34.92 Y0))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 (binintersect( 236.86/34.92 Y0, Y1) = 236.86/34.92 Y0)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (( 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1) = 236.86/34.92 Y1) => 236.86/34.92 subset( 236.86/34.92 Y1, Y0)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1)) => 236.86/34.92 in(Y2, 236.86/34.92 Y1))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (( 236.86/34.92 ~(( 236.86/34.92 ??(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) & 236.86/34.92 in(Y2, 236.86/34.92 Y1))))))) => 236.86/34.92 (binintersect( 236.86/34.92 Y0, Y1) = 236.86/34.92 emptyset)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 subset( 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1), 236.86/34.92 Y1))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y1, Y0) => 236.86/34.92 (binintersect( 236.86/34.92 Y0, Y1) = 236.86/34.92 Y1)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (( 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1) = 236.86/34.92 Y0) => 236.86/34.92 subset( 236.86/34.92 Y0, Y1)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (binintersect( 236.86/34.92 Y0, 236.86/34.92 binunion( 236.86/34.92 Y1, Y2)) = 236.86/34.92 binunion( 236.86/34.92 binintersect( 236.86/34.92 Y0, Y1), 236.86/34.92 binintersect( 236.86/34.92 Y0, Y2)))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 in(Y2, 236.86/34.92 setminus( 236.86/34.92 Y0, Y1))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 setminus( 236.86/34.92 Y0, Y1)) => 236.86/34.92 in(Y2, 236.86/34.92 Y0))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 setminus( 236.86/34.92 Y0, Y1)) => 236.86/34.92 (~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (subset( 236.86/34.92 Y0, Y1) => 236.86/34.92 (setminus( 236.86/34.92 Y0, Y1) = 236.86/34.92 emptyset)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 setminus( 236.86/34.92 Y0, Y1)))) => 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 in(Y2, 236.86/34.92 Y1)))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 setminus( 236.86/34.92 Y0, Y1)))) => 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 (~( 236.86/34.92 in(Y2, 236.86/34.92 Y0)))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y0))) => 236.86/34.92 (~( 236.86/34.92 in(Y2, 236.86/34.92 setminus( 236.86/34.92 Y0, Y1)))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y1) => 236.86/34.92 (~( 236.86/34.92 in(Y2, 236.86/34.92 setminus( 236.86/34.92 Y0, Y1)))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 subset( 236.86/34.92 setminus( 236.86/34.92 Y0, Y1), 236.86/34.92 Y0))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (( 236.86/34.92 setminus( 236.86/34.92 Y0, Y1) = 236.86/34.92 emptyset) => 236.86/34.92 subset( 236.86/34.92 Y0, Y1)))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 symdiff( 236.86/34.92 Y0, Y1)) => 236.86/34.92 (!!(( 236.86/34.92 ^[Y3 : $o]: 236.86/34.92 (( 236.86/34.92 in(Y2, 236.86/34.92 Y0) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 Y3)) => 236.86/34.92 (( 236.86/34.92 ( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y0))) => 236.86/34.92 ( 236.86/34.92 in(Y2, 236.86/34.92 Y1) => Y3)) => 236.86/34.92 Y3))))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 in(Y2, 236.86/34.92 symdiff( 236.86/34.92 Y0, Y1))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y0))) => 236.86/34.92 (in(Y2, 236.86/34.92 Y1) => 236.86/34.92 in(Y2, 236.86/34.92 symdiff( 236.86/34.92 Y0, Y1))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 Y0) => 236.86/34.92 (in(Y2, 236.86/34.92 Y1) => 236.86/34.92 (~( 236.86/34.92 in(Y2, 236.86/34.92 symdiff( 236.86/34.92 Y0, Y1))))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y0))) => 236.86/34.92 (( 236.86/34.92 ~( 236.86/34.92 in(Y2, 236.86/34.92 Y1))) => 236.86/34.92 (~( 236.86/34.92 in(Y2, 236.86/34.92 symdiff( 236.86/34.92 Y0, Y1))))))))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 in(Y1, 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 setadjoin( 236.86/34.92 Y1, 236.86/34.92 emptyset))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 in(Y0, 236.86/34.92 setunion( 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 emptyset), 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 setadjoin( 236.86/34.92 Y1, 236.86/34.92 emptyset)), 236.86/34.92 emptyset)))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 in(Y1, 236.86/34.92 setunion( 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 emptyset), 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 setadjoin( 236.86/34.92 Y1, 236.86/34.92 emptyset)), 236.86/34.92 emptyset)))))))))) => 236.86/34.92 ( 236.86/34.92 ( 236.86/34.92 !!(( 236.86/34.92 ^[Y0 : $i]: 236.86/34.92 (!!(( 236.86/34.92 ^[Y1 : $i]: 236.86/34.92 (??(( 236.86/34.92 ^[Y2 : $i]: 236.86/34.92 (in(Y2, 236.86/34.92 setunion( 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 emptyset), 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 setadjoin( 236.86/34.92 Y1, 236.86/34.92 emptyset)), 236.86/34.92 emptyset)))) & 236.86/34.92 (??(( 236.86/34.92 ^[Y3 : $i]: 236.86/34.92 (in(Y3, 236.86/34.92 setunion( 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 emptyset), 236.86/34.92 setadjoin( 236.86/34.92 setadjoin( 236.86/34.92 Y0, 236.86/34.92 setadjoin( 236.86/34.92 Y1, 236.86/34.92 emptyset)), 236.86/34.92 emptyset)))) & 236.86/34.92 (setadjoin( 236.86/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)) = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)) = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 Y0) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset), 237.08/34.92 Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 Y0) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset), 237.08/34.92 powerset( 237.08/34.92 Y0))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))) => 237.08/34.92 (( 237.08/34.92 Y2 = Y1) | 237.08/34.92 (Y2 = Y0)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) & 237.08/34.92 (??(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 Y1) & 237.08/34.92 (Y2 = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 setadjoin( 237.08/34.92 Y4, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 Y2)) & 237.08/34.92 (??(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 setunion( 237.08/34.92 Y2)) & 237.08/34.92 (Y2 = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 setadjoin( 237.08/34.92 Y4, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 setunion( 237.08/34.92 Y0)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 in(Y1, 237.08/34.92 Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 subset( 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)), 237.08/34.92 Y0)))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)) = 237.08/34.92 Y0)))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y2) => 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))))) => 237.08/34.92 (( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 Y1(Y2))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset)))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 Y1(Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y2) => 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y3 = Y2)))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.92 inference('lazy_cnf_imply', [status(thm)], ['200'])). 237.08/34.92 tff('202', plain, 237.08/34.92 ~ ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, setadjoin(Y0, Y1)) => 237.08/34.92 (in(Y2, Y1) | (Y2 = Y0)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 237.08/34.92 in(Y1, powerset(Y0))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.92 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y1, powerset(Y0)) => 237.08/34.92 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y1, Y2) => 237.08/34.92 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y1, setunion(Y0)) => 237.08/34.92 (!!((^[Y2 : $o]: 237.08/34.92 ((!!((^[Y3 : $i]: 237.08/34.92 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.92 Y2))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 != Y1) => 237.08/34.92 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.92 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setadjoin(Y0, 237.08/34.92 setadjoin(Y1, emptyset))) => 237.08/34.92 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin(Y0, 237.08/34.92 setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.92 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.92 (~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.92 (~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $o]: 237.08/34.92 (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.92 ((!!((^[Y0 : $o]: 237.08/34.92 (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & 237.08/34.92 Y1(Y2))))))) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 Y1(Y2))))))) => 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & 237.08/34.92 (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??(Y0)) => 237.08/34.92 ((!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) <=> 237.08/34.92 (Y2 = Y1)))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 ((Y2 = Y3) => 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y3, 237.08/34.92 Y1)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (( 237.08/34.92 Y2 = Y3) => 237.08/34.92 ( 237.08/34.92 in(Y2, 237.08/34.92 Y0) <=> 237.08/34.92 in(Y3, 237.08/34.92 Y1)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))) => 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (( 237.08/34.92 Y2 = Y3) => 237.08/34.92 (Y0(Y2) <=> 237.08/34.92 Y1(Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) & 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y0(Y3) => 237.08/34.92 ( 237.08/34.92 Y2 = Y3))))))))) <=> 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (Y1(Y2) & 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y1(Y3) => 237.08/34.92 ( 237.08/34.92 Y2 = Y3))))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (( 237.08/34.92 Y2 = Y3) => 237.08/34.92 (setadjoin( 237.08/34.92 Y0, Y2) = 237.08/34.92 setadjoin( 237.08/34.92 Y1, Y3)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (powerset(Y0) = 237.08/34.92 powerset(Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (setunion(Y0) = 237.08/34.92 setunion(Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 ( 237.08/34.92 Y1 = Y2))))))))) => 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 ( 237.08/34.92 Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (( 237.08/34.92 Y2 = Y3) => 237.08/34.92 (Y0(Y2) <=> 237.08/34.92 Y1(Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 ( 237.08/34.92 Y0(Y2) & 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y0(Y3) => 237.08/34.92 (Y2 = Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (Y1(Y2) & 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))) => 237.08/34.92 (descr(Y0) = 237.08/34.92 descr(Y1))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i > $o]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i > $o]: 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y5 : $i]: 237.08/34.92 (in(Y5, 237.08/34.92 Y1) => 237.08/34.92 (( 237.08/34.92 Y4 = Y5) => 237.08/34.92 (Y2(Y4) <=> 237.08/34.92 Y3(Y5))))))))))) => 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y2) = 237.08/34.92 dsetconstr( 237.08/34.92 Y1, Y3)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))) => 237.08/34.92 subset(Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 subset(Y1, Y0)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 subset(Y0, 237.08/34.92 Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 ( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))) => 237.08/34.92 subset(Y0, 237.08/34.92 Y1)))))))) => 237.08/34.92 ((!!(subset(emptyset))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 subset( 237.08/34.92 Y0, Y1))) => 237.08/34.92 (Y0 != Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (Y0 != Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 subset(Y0, 237.08/34.92 Y0)))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (subset( 237.08/34.92 Y1, Y2) => 237.08/34.92 subset( 237.08/34.92 Y0, Y2)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y2) => 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, Y2)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 in(Y0, 237.08/34.92 powerset( 237.08/34.92 Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 (Y0 = Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, 237.08/34.92 emptyset) => 237.08/34.92 (Y0 = 237.08/34.92 emptyset))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 in(Y1, 237.08/34.92 powerset( 237.08/34.92 Y0))))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 powerset( 237.08/34.92 Y0)) => 237.08/34.92 subset( 237.08/34.92 Y1, Y0)))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 powerset( 237.08/34.92 Y0))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 subset( 237.08/34.92 powerset( 237.08/34.92 Y0), 237.08/34.92 powerset( 237.08/34.92 Y1))))))))) => 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 in( 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1), 237.08/34.92 powerset( 237.08/34.92 Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 subset( 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $o]: 237.08/34.92 (in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => Y3) => 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y1) => Y3) => 237.08/34.92 Y3))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) | 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y1, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y2, Y0) => 237.08/34.92 (subset( 237.08/34.92 Y2, Y1) => 237.08/34.92 subset( 237.08/34.92 Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y0))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 Y1, Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 ~(( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 Y1))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y0) => 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (binintersect( 237.08/34.92 Y0, 237.08/34.92 binunion( 237.08/34.92 Y1, Y2)) = 237.08/34.92 binunion( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 binintersect( 237.08/34.92 Y0, Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y0))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (setminus( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))) => 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 setminus( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 setminus( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset) => 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $o]: 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 Y3)) => 237.08/34.92 (( 237.08/34.92 ( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 ( 237.08/34.92 in(Y2, 237.08/34.92 Y1) => Y3)) => 237.08/34.92 Y3))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)) = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)) = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 Y0) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset), 237.08/34.92 Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 Y0) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset), 237.08/34.92 powerset( 237.08/34.92 Y0))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))) => 237.08/34.92 (( 237.08/34.92 Y2 = Y1) | 237.08/34.92 (Y2 = Y0)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) & 237.08/34.92 (??(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 Y1) & 237.08/34.92 (Y2 = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 setadjoin( 237.08/34.92 Y4, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 Y2)) & 237.08/34.92 (??(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 setunion( 237.08/34.92 Y2)) & 237.08/34.92 (Y2 = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 setadjoin( 237.08/34.92 Y4, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 setunion( 237.08/34.92 Y0)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 in(Y1, 237.08/34.92 Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 subset( 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)), 237.08/34.92 Y0)))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)) = 237.08/34.92 Y0)))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y2) => 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))))) => 237.08/34.92 (( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 Y1(Y2))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset)))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 Y1(Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y2) => 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y3 = Y2)))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.92 inference('lazy_cnf_imply', [status(thm)], ['201'])). 237.08/34.92 tff('203', plain, 237.08/34.92 ~ ((!!((^[Y0 : $i]: (dsetconstr(Y0, (^[Y1 : $i]: $true)) = Y0)))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 237.08/34.92 in(Y1, powerset(Y0))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.92 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y1, powerset(Y0)) => 237.08/34.92 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y1, Y2) => 237.08/34.92 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y1, setunion(Y0)) => 237.08/34.92 (!!((^[Y2 : $o]: 237.08/34.92 ((!!((^[Y3 : $i]: 237.08/34.92 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.92 Y2))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 != Y1) => 237.08/34.92 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.92 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setadjoin(Y0, 237.08/34.92 setadjoin(Y1, emptyset))) => 237.08/34.92 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.92 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.92 (~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.92 (~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $o]: 237.08/34.92 (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.92 ((!!((^[Y0 : $o]: 237.08/34.92 (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 Y1(Y2))))))) => 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & 237.08/34.92 (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??(Y0)) => 237.08/34.92 ((!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) <=> 237.08/34.92 (Y2 = Y1)))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 ((Y2 = Y3) => 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 in(Y3, Y1)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 ((Y2 = Y3) => 237.08/34.92 (in(Y2, 237.08/34.92 Y0) <=> 237.08/34.92 in(Y3, 237.08/34.92 Y1)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))) => 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 Y2 = Y3) => 237.08/34.92 ( 237.08/34.92 Y0(Y2) <=> 237.08/34.92 Y1(Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) & 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (Y0(Y3) => 237.08/34.92 (Y2 = Y3))))))))) <=> 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (Y1(Y2) & 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (( 237.08/34.92 Y2 = Y3) => 237.08/34.92 (setadjoin( 237.08/34.92 Y0, Y2) = 237.08/34.92 setadjoin( 237.08/34.92 Y1, Y3)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (powerset(Y0) = 237.08/34.92 powerset(Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (setunion(Y0) = 237.08/34.92 setunion(Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))) => 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (( 237.08/34.92 Y2 = Y3) => 237.08/34.92 (Y0(Y2) <=> 237.08/34.92 Y1(Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) & 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y0(Y3) => 237.08/34.92 (Y2 = Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 ( 237.08/34.92 Y1(Y2) & 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))) => 237.08/34.92 (descr(Y0) = 237.08/34.92 descr(Y1))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i > $o]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i > $o]: 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y5 : $i]: 237.08/34.92 (in(Y5, 237.08/34.92 Y1) => 237.08/34.92 (( 237.08/34.92 Y4 = Y5) => 237.08/34.92 (Y2(Y4) <=> 237.08/34.92 Y3(Y5))))))))))) => 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y2) = 237.08/34.92 dsetconstr( 237.08/34.92 Y1, Y3)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 ( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))) => 237.08/34.92 subset(Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 subset(Y1, Y0)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 subset(Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))) => 237.08/34.92 subset(Y0, 237.08/34.92 Y1)))))))) => 237.08/34.92 ((!!(subset(emptyset))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 ( 237.08/34.92 subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 ( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 ~( 237.08/34.92 subset( 237.08/34.92 Y0, Y1))) => 237.08/34.92 ( 237.08/34.92 Y0 != Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (Y0 != Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 subset(Y0, Y0)))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (subset( 237.08/34.92 Y1, Y2) => 237.08/34.92 subset( 237.08/34.92 Y0, Y2)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y2) => 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, Y2)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 in(Y0, 237.08/34.92 powerset( 237.08/34.92 Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 (Y0 = Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, 237.08/34.92 emptyset) => 237.08/34.92 (Y0 = 237.08/34.92 emptyset))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 in(Y1, 237.08/34.92 powerset( 237.08/34.92 Y0))))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 powerset( 237.08/34.92 Y0)) => 237.08/34.92 subset( 237.08/34.92 Y1, Y0)))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 powerset( 237.08/34.92 Y0))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 subset( 237.08/34.92 powerset( 237.08/34.92 Y0), 237.08/34.92 powerset( 237.08/34.92 Y1))))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 in( 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1), 237.08/34.92 powerset( 237.08/34.92 Y0)))))))) => 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 subset( 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $o]: 237.08/34.92 (in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => Y3) => 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y1) => Y3) => 237.08/34.92 Y3))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) | 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y1, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y2, Y0) => 237.08/34.92 (subset( 237.08/34.92 Y2, Y1) => 237.08/34.92 subset( 237.08/34.92 Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y0))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 Y1, Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 ~(( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 Y1))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y0) => 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (binintersect( 237.08/34.92 Y0, 237.08/34.92 binunion( 237.08/34.92 Y1, Y2)) = 237.08/34.92 binunion( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 binintersect( 237.08/34.92 Y0, Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y0))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (setminus( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))) => 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 setminus( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 setminus( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset) => 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $o]: 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 Y3)) => 237.08/34.92 (( 237.08/34.92 ( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 ( 237.08/34.92 in(Y2, 237.08/34.92 Y1) => Y3)) => 237.08/34.92 Y3))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 symdiff( 237.08/34.92 Y0, Y1))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)) = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)))) & 237.08/34.92 (setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)) = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 Y0) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset), 237.08/34.92 Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 Y0) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset), 237.08/34.92 powerset( 237.08/34.92 Y0))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))) => 237.08/34.92 (( 237.08/34.92 Y2 = Y1) | 237.08/34.92 (Y2 = Y0)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 powerset( 237.08/34.92 powerset( 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y1) => 237.08/34.92 in( 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset)), 237.08/34.92 emptyset)), 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) & 237.08/34.92 (??(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 Y1) & 237.08/34.92 (Y2 = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 setadjoin( 237.08/34.92 Y4, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 cartprod( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 setunion( 237.08/34.92 Y2)) & 237.08/34.92 (??(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 setunion( 237.08/34.92 Y2)) & 237.08/34.92 (Y2 = 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset), 237.08/34.92 setadjoin( 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 setadjoin( 237.08/34.92 Y4, 237.08/34.92 emptyset)), 237.08/34.92 emptyset))))))))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 setunion( 237.08/34.92 Y0)) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 in(Y1, 237.08/34.92 Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 subset( 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)), 237.08/34.92 Y0)))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (setunion( 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 emptyset)) = 237.08/34.92 Y0)))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y2) => 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))))) => 237.08/34.92 (( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 Y1(Y2))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y2, 237.08/34.92 emptyset)))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 Y1(Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y2) => 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 Y0) => 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y3 = Y2)))))) => 237.08/34.92 (??(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (in(Y3, 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1)) & 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y1) = 237.08/34.92 setadjoin( 237.08/34.92 Y3, 237.08/34.92 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.92 inference('lazy_cnf_imply', [status(thm)], ['202'])). 237.08/34.92 tff('204', plain, 237.08/34.92 ~ ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!((^[Y2 : $i]: (in(Y2, Y1) => in(Y2, Y0))))) => 237.08/34.92 in(Y1, powerset(Y0))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.92 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y1, powerset(Y0)) => 237.08/34.92 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y1, Y2) => 237.08/34.92 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y1, setunion(Y0)) => 237.08/34.92 (!!((^[Y2 : $o]: 237.08/34.92 ((!!((^[Y3 : $i]: 237.08/34.92 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.92 Y2))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 != Y1) => 237.08/34.92 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.92 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setadjoin(Y0, 237.08/34.92 setadjoin(Y1, emptyset))) => 237.08/34.92 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.92 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.92 (~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.92 (~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $o]: 237.08/34.92 (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.92 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((~((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 Y1(Y2))))))) => 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (in(Y2, Y0) & 237.08/34.92 (~(Y1(Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??(Y0)) => 237.08/34.92 ((!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.92 (??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 ((Y2 = Y3) => 237.08/34.92 (in(Y2, Y0) => 237.08/34.92 in(Y3, Y1)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 ((Y2 = Y3) => 237.08/34.92 (in(Y2, Y0) <=> 237.08/34.92 in(Y3, Y1)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))) => 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (( 237.08/34.92 Y2 = Y3) => 237.08/34.92 ( 237.08/34.92 Y0(Y2) <=> 237.08/34.92 Y1(Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) & 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (Y0(Y3) => 237.08/34.92 (Y2 = Y3))))))))) <=> 237.08/34.92 (??((^[Y2 : $i]: 237.08/34.92 (Y1(Y2) & 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (!!((^[Y3 : $i]: 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 Y2 = Y3) => 237.08/34.92 ( 237.08/34.92 setadjoin( 237.08/34.92 Y0, Y2) = 237.08/34.92 setadjoin( 237.08/34.92 Y1, Y3)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (powerset(Y0) = 237.08/34.92 powerset(Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (setunion(Y0) = 237.08/34.92 setunion(Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 ((??((^[Y1 : $i]: 237.08/34.92 (Y0(Y1) & 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))) => 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!((^[Y2 : $i]: 237.08/34.92 (Y0(Y1) => 237.08/34.92 (Y0(Y2) => 237.08/34.92 (Y1 = Y2))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i > $o]: 237.08/34.92 (!!((^[Y1 : $i > $o]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 Y2 = Y3) => 237.08/34.92 ( 237.08/34.92 Y0(Y2) <=> 237.08/34.92 Y1(Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (Y0(Y2) & 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y0(Y3) => 237.08/34.92 (Y2 = Y3))))))))) => 237.08/34.92 ((??((^[Y2 : $i]: 237.08/34.92 (Y1(Y2) & 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y3 : $i]: 237.08/34.92 (Y1(Y3) => 237.08/34.92 (Y2 = Y3))))))))) => 237.08/34.92 (descr(Y0) = 237.08/34.92 descr(Y1))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 (!!((^[Y2 : $i > $o]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $i > $o]: 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y4 : $i]: 237.08/34.92 (in(Y4, 237.08/34.92 Y0) => 237.08/34.92 (!!(( 237.08/34.92 ^[Y5 : $i]: 237.08/34.92 (in(Y5, 237.08/34.92 Y1) => 237.08/34.92 (( 237.08/34.92 Y4 = Y5) => 237.08/34.92 (Y2(Y4) <=> 237.08/34.92 Y3(Y5))))))))))) => 237.08/34.92 (dsetconstr( 237.08/34.92 Y0, Y2) = 237.08/34.92 dsetconstr( 237.08/34.92 Y1, Y3)))))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))) => 237.08/34.92 subset(Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 subset(Y1, Y0)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((Y0 = Y1) => 237.08/34.92 subset(Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ((!!((^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))) => 237.08/34.92 subset(Y0, Y1)))))))) => 237.08/34.92 ((!!(subset(emptyset))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 ( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 ( 237.08/34.92 subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 ( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 subset( 237.08/34.92 Y0, Y1))) => 237.08/34.92 ( 237.08/34.92 Y0 != Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (Y0 != Y1)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 subset(Y0, Y0)))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!((^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (subset( 237.08/34.92 Y1, Y2) => 237.08/34.92 subset( 237.08/34.92 Y0, Y2)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y2) => 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, Y2)))))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 in(Y0, 237.08/34.92 powerset( 237.08/34.92 Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 (Y0 = Y1))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 ( 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 emptyset) => 237.08/34.92 ( 237.08/34.92 Y0 = 237.08/34.92 emptyset))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 in(Y1, 237.08/34.92 powerset( 237.08/34.92 Y0))))))))) => 237.08/34.92 ((!!((^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (in(Y1, 237.08/34.92 powerset( 237.08/34.92 Y0)) => 237.08/34.92 subset( 237.08/34.92 Y1, Y0)))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 in(Y0, 237.08/34.92 powerset( 237.08/34.92 Y0))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 subset( 237.08/34.92 powerset( 237.08/34.92 Y0), 237.08/34.92 powerset( 237.08/34.92 Y1))))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 in( 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1), 237.08/34.92 powerset( 237.08/34.92 Y0)))))))) => 237.08/34.92 ((!!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i > $o]: 237.08/34.92 subset( 237.08/34.92 dsetconstr( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 (( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 in(Y1, 237.08/34.92 setadjoin( 237.08/34.92 Y0, 237.08/34.92 setadjoin( 237.08/34.92 Y1, 237.08/34.92 emptyset))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y3 : $o]: 237.08/34.92 (in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y0) => Y3) => 237.08/34.92 (( 237.08/34.92 in(Y2, 237.08/34.92 Y1) => Y3) => 237.08/34.92 Y3))))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) | 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y0, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 Y1, 237.08/34.92 binunion( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y2, Y0) => 237.08/34.92 (subset( 237.08/34.92 Y2, Y1) => 237.08/34.92 subset( 237.08/34.92 Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y0))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y1) => 237.08/34.92 subset( 237.08/34.92 Y1, Y0)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 ~(( 237.08/34.92 ??(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) & 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 Y1))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y1, Y0) => 237.08/34.92 (binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1) = 237.08/34.92 Y0) => 237.08/34.92 subset( 237.08/34.92 Y0, Y1)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (binintersect( 237.08/34.92 Y0, 237.08/34.92 binunion( 237.08/34.92 Y1, Y2)) = 237.08/34.92 binunion( 237.08/34.92 binintersect( 237.08/34.92 Y0, Y1), 237.08/34.92 binintersect( 237.08/34.92 Y0, Y2)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)) => 237.08/34.92 in(Y2, 237.08/34.92 Y0))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (subset( 237.08/34.92 Y0, Y1) => 237.08/34.92 (setminus( 237.08/34.92 Y0, Y1) = 237.08/34.92 emptyset)))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))) => 237.08/34.92 (in(Y2, 237.08/34.92 Y0) => 237.08/34.92 in(Y2, 237.08/34.92 Y1)))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))) => 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y1))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 Y0)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (( 237.08/34.92 ~( 237.08/34.92 in(Y2, 237.08/34.92 Y0))) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y2 : $i]: 237.08/34.92 (in(Y2, 237.08/34.92 Y1) => 237.08/34.92 (~( 237.08/34.92 in(Y2, 237.08/34.92 setminus( 237.08/34.92 Y0, Y1)))))))))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 subset( 237.08/34.92 setminus( 237.08/34.92 Y0, Y1), 237.08/34.92 Y0))))))) => 237.08/34.92 ( 237.08/34.92 ( 237.08/34.92 !!(( 237.08/34.92 ^[Y0 : $i]: 237.08/34.92 (!!(( 237.08/34.92 ^[Y1 : $i]: 237.08/34.92 (( 237.08/34.92 setminus( 237.08/34.92 Y0, Y1) = 237.08/34.93 emptyset) => 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $o]: 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 Y3)) => 237.08/34.93 (( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y1) => Y3)) => 237.08/34.93 Y3))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 Y0))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))) => 237.08/34.93 (( 237.08/34.93 Y2 = Y1) | 237.08/34.93 (Y2 = Y0)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 Y1) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 setunion( 237.08/34.93 Y0)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 in(Y1, 237.08/34.93 Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)), 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)) = 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y2 = Y3))))))))))) => 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y3 = Y2)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.93 inference('lazy_cnf_imply', [status(thm)], ['203'])). 237.08/34.93 tff('205', plain, 237.08/34.93 ~ ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.93 ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y1, powerset(Y0)) => 237.08/34.93 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y1, Y2) => 237.08/34.93 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, setunion(Y0)) => 237.08/34.93 (!!((^[Y2 : $o]: 237.08/34.93 ((!!((^[Y3 : $i]: 237.08/34.93 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.93 Y2))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 != Y1) => 237.08/34.93 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.93 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin(Y0, 237.08/34.93 setadjoin(Y1, emptyset))) => 237.08/34.93 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.93 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.93 (~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.93 (~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $o]: 237.08/34.93 (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => 237.08/34.93 (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & 237.08/34.93 (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??(Y0)) => 237.08/34.93 ((!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (in(Y2, Y0) => 237.08/34.93 in(Y3, Y1)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (in(Y2, Y0) <=> 237.08/34.93 in(Y3, Y1)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))) => 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (Y0(Y2) <=> 237.08/34.93 Y1(Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) & 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ( 237.08/34.93 Y0(Y3) => 237.08/34.93 ( 237.08/34.93 Y2 = Y3))))))))) <=> 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (Y1(Y2) & 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ( 237.08/34.93 Y1(Y3) => 237.08/34.93 ( 237.08/34.93 Y2 = Y3))))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 (( 237.08/34.93 Y2 = Y3) => 237.08/34.93 ( 237.08/34.93 setadjoin( 237.08/34.93 Y0, Y2) = 237.08/34.93 setadjoin( 237.08/34.93 Y1, Y3)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (powerset(Y0) = 237.08/34.93 powerset(Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (setunion(Y0) = 237.08/34.93 setunion(Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))) => 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (( 237.08/34.93 Y2 = Y3) => 237.08/34.93 ( 237.08/34.93 Y0(Y2) <=> 237.08/34.93 Y1(Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) & 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (Y0(Y3) => 237.08/34.93 (Y2 = Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y1(Y2) & 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y2 = Y3))))))))) => 237.08/34.93 (descr(Y0) = 237.08/34.93 descr(Y1))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i > $o]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i > $o]: 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y5 : $i]: 237.08/34.93 (in(Y5, 237.08/34.93 Y1) => 237.08/34.93 (( 237.08/34.93 Y4 = Y5) => 237.08/34.93 (Y2(Y4) <=> 237.08/34.93 Y3(Y5))))))))))) => 237.08/34.93 ( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y2) = 237.08/34.93 dsetconstr( 237.08/34.93 Y1, Y3)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => 237.08/34.93 in(Y2, Y1))))) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 subset(Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1))))) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!(subset(emptyset))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((~( 237.08/34.93 subset( 237.08/34.93 Y0, Y1))) => 237.08/34.93 (Y0 != Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (Y0 != Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 subset(Y0, Y0)))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (subset( 237.08/34.93 Y1, Y2) => 237.08/34.93 subset( 237.08/34.93 Y0, Y2)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y2) => 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, Y2)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 ( 237.08/34.93 subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 in(Y0, 237.08/34.93 powerset( 237.08/34.93 Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 (Y0 = Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, 237.08/34.93 emptyset) => 237.08/34.93 ( 237.08/34.93 Y0 = 237.08/34.93 emptyset))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 in(Y1, 237.08/34.93 powerset( 237.08/34.93 Y0))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 powerset( 237.08/34.93 Y0)) => 237.08/34.93 subset( 237.08/34.93 Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 powerset( 237.08/34.93 Y0))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 subset( 237.08/34.93 powerset( 237.08/34.93 Y0), 237.08/34.93 powerset( 237.08/34.93 Y1))))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 in( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1), 237.08/34.93 powerset( 237.08/34.93 Y0)))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 subset( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))) => 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $o]: 237.08/34.93 (in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => Y3) => 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y1) => Y3) => 237.08/34.93 Y3))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) | 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y1, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y2, Y0) => 237.08/34.93 (subset( 237.08/34.93 Y2, Y1) => 237.08/34.93 subset( 237.08/34.93 Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y0))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 Y1, Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 ~(( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 Y1))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y0) => 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (binintersect( 237.08/34.93 Y0, 237.08/34.93 binunion( 237.08/34.93 Y1, Y2)) = 237.08/34.93 binunion( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 binintersect( 237.08/34.93 Y0, Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y0))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (setminus( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))) => 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 setminus( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 setminus( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset) => 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $o]: 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 Y3)) => 237.08/34.93 (( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y1) => Y3)) => 237.08/34.93 Y3))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 Y0))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))) => 237.08/34.93 (( 237.08/34.93 Y2 = Y1) | 237.08/34.93 (Y2 = Y0)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 Y1) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 setunion( 237.08/34.93 Y0)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 in(Y1, 237.08/34.93 Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)), 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)) = 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y2 = Y3))))))))))) => 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y3 = Y2)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.93 inference('lazy_cnf_imply', [status(thm)], ['204'])). 237.08/34.93 tff('206', plain, 237.08/34.93 ~ ((!!((^[Y0 : $i]: in(emptyset, powerset(Y0))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y1, powerset(Y0)) => 237.08/34.93 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y1, Y2) => 237.08/34.93 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, setunion(Y0)) => 237.08/34.93 (!!((^[Y2 : $o]: 237.08/34.93 ((!!((^[Y3 : $i]: 237.08/34.93 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.93 Y2))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 != Y1) => 237.08/34.93 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.93 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin(Y0, 237.08/34.93 setadjoin(Y1, emptyset))) => 237.08/34.93 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.93 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.93 (~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.93 (~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $o]: 237.08/34.93 (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??(Y0)) => 237.08/34.93 ((!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (in(Y2, Y0) => 237.08/34.93 in(Y3, Y1)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (in(Y2, Y0) <=> 237.08/34.93 in(Y3, Y1)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))) => 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (Y0(Y2) <=> 237.08/34.93 Y1(Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) & 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 (Y0(Y3) => 237.08/34.93 ( 237.08/34.93 Y2 = Y3))))))))) <=> 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (Y1(Y2) & 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 (Y1(Y3) => 237.08/34.93 ( 237.08/34.93 Y2 = Y3))))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (setadjoin( 237.08/34.93 Y0, Y2) = 237.08/34.93 setadjoin( 237.08/34.93 Y1, Y3)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (powerset(Y0) = 237.08/34.93 powerset(Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (setunion(Y0) = 237.08/34.93 setunion(Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))) => 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 (( 237.08/34.93 Y2 = Y3) => 237.08/34.93 (Y0(Y2) <=> 237.08/34.93 Y1(Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) & 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 ( 237.08/34.93 Y0(Y3) => 237.08/34.93 ( 237.08/34.93 Y2 = Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y1(Y2) & 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y2 = Y3))))))))) => 237.08/34.93 (descr(Y0) = 237.08/34.93 descr(Y1))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i > $o]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i > $o]: 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y5 : $i]: 237.08/34.93 (in(Y5, 237.08/34.93 Y1) => 237.08/34.93 (( 237.08/34.93 Y4 = Y5) => 237.08/34.93 (Y2(Y4) <=> 237.08/34.93 Y3(Y5))))))))))) => 237.08/34.93 ( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y2) = 237.08/34.93 dsetconstr( 237.08/34.93 Y1, Y3)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => 237.08/34.93 in(Y2, Y1))))) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 subset(Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1))))) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!(subset(emptyset))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((~( 237.08/34.93 subset( 237.08/34.93 Y0, Y1))) => 237.08/34.93 (Y0 != Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (Y0 != Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 subset(Y0, Y0)))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (subset( 237.08/34.93 Y1, Y2) => 237.08/34.93 subset( 237.08/34.93 Y0, Y2)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y2) => 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, Y2)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 in(Y0, 237.08/34.93 powerset( 237.08/34.93 Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 ( 237.08/34.93 subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 ( 237.08/34.93 subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 ( 237.08/34.93 Y0 = Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, 237.08/34.93 emptyset) => 237.08/34.93 (Y0 = 237.08/34.93 emptyset))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 in(Y1, 237.08/34.93 powerset( 237.08/34.93 Y0))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 powerset( 237.08/34.93 Y0)) => 237.08/34.93 subset( 237.08/34.93 Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 powerset( 237.08/34.93 Y0))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 subset( 237.08/34.93 powerset( 237.08/34.93 Y0), 237.08/34.93 powerset( 237.08/34.93 Y1))))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 in( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1), 237.08/34.93 powerset( 237.08/34.93 Y0)))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 subset( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))))))))) => 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $o]: 237.08/34.93 (in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => Y3) => 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y1) => Y3) => 237.08/34.93 Y3))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) | 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y1, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y2, Y0) => 237.08/34.93 (subset( 237.08/34.93 Y2, Y1) => 237.08/34.93 subset( 237.08/34.93 Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y0))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 Y1, Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 ~(( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 Y1))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y0) => 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (binintersect( 237.08/34.93 Y0, 237.08/34.93 binunion( 237.08/34.93 Y1, Y2)) = 237.08/34.93 binunion( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 binintersect( 237.08/34.93 Y0, Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y0))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (setminus( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))) => 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 setminus( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 setminus( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset) => 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $o]: 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 Y3)) => 237.08/34.93 (( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y1) => Y3)) => 237.08/34.93 Y3))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 Y0))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))) => 237.08/34.93 (( 237.08/34.93 Y2 = Y1) | 237.08/34.93 (Y2 = Y0)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 Y1) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 setunion( 237.08/34.93 Y0)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 in(Y1, 237.08/34.93 Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)), 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)) = 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y2 = Y3))))))))))) => 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y3 = Y2)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.93 inference('lazy_cnf_imply', [status(thm)], ['205'])). 237.08/34.93 tff('207', plain, 237.08/34.93 ~ ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y1, powerset(Y0)) => 237.08/34.93 (in(Y2, Y1) => in(Y2, Y0)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y1, Y2) => 237.08/34.93 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, setunion(Y0)) => 237.08/34.93 (!!((^[Y2 : $o]: 237.08/34.93 ((!!((^[Y3 : $i]: 237.08/34.93 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.93 Y2))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 != Y1) => 237.08/34.93 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.93 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin(Y0, 237.08/34.93 setadjoin(Y1, emptyset))) => 237.08/34.93 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.93 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.93 (~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.93 (~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??(Y0)) => 237.08/34.93 ((!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (in(Y2, Y0) => 237.08/34.93 in(Y3, Y1)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (in(Y2, Y0) <=> 237.08/34.93 in(Y3, Y1)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (Y0(Y2) <=> 237.08/34.93 Y1(Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) & 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 (Y0(Y3) => 237.08/34.93 (Y2 = Y3))))))))) <=> 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (Y1(Y2) & 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y2 = Y3))))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 ((Y2 = Y3) => 237.08/34.93 (setadjoin( 237.08/34.93 Y0, Y2) = 237.08/34.93 setadjoin( 237.08/34.93 Y1, Y3)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (powerset(Y0) = 237.08/34.93 powerset(Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (setunion(Y0) = 237.08/34.93 setunion(Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))) => 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => 237.08/34.93 (Y1 = Y2))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (!!((^[Y3 : $i]: 237.08/34.93 (( 237.08/34.93 Y2 = Y3) => 237.08/34.93 (Y0(Y2) <=> 237.08/34.93 Y1(Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) & 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (Y0(Y3) => 237.08/34.93 ( 237.08/34.93 Y2 = Y3))))))))) => 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (Y1(Y2) & 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 ( 237.08/34.93 Y1(Y3) => 237.08/34.93 ( 237.08/34.93 Y2 = Y3))))))))) => 237.08/34.93 (descr(Y0) = 237.08/34.93 descr(Y1))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 (!!((^[Y2 : $i > $o]: 237.08/34.93 (!!((^[Y3 : $i > $o]: 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y5 : $i]: 237.08/34.93 (in(Y5, 237.08/34.93 Y1) => 237.08/34.93 (( 237.08/34.93 Y4 = Y5) => 237.08/34.93 (Y2(Y4) <=> 237.08/34.93 Y3(Y5))))))))))) => 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y2) = 237.08/34.93 dsetconstr( 237.08/34.93 Y1, Y3)))))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => 237.08/34.93 in(Y2, Y1))))) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 subset(Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1))))) => 237.08/34.93 subset(Y0, Y1)))))))) => 237.08/34.93 ((!!(subset(emptyset))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 ( 237.08/34.93 subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((~(subset( 237.08/34.93 Y0, Y1))) => 237.08/34.93 (Y0 != Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 ( 237.08/34.93 Y0 != Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 subset(Y0, Y0)))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (subset( 237.08/34.93 Y1, Y2) => 237.08/34.93 subset( 237.08/34.93 Y0, Y2)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y2) => 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, Y2)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 in(Y0, 237.08/34.93 powerset( 237.08/34.93 Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 ( 237.08/34.93 subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 ( 237.08/34.93 Y0 = Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (subset(Y0, 237.08/34.93 emptyset) => 237.08/34.93 (Y0 = 237.08/34.93 emptyset))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 in(Y1, 237.08/34.93 powerset( 237.08/34.93 Y0))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 powerset( 237.08/34.93 Y0)) => 237.08/34.93 subset( 237.08/34.93 Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 powerset( 237.08/34.93 Y0))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 subset( 237.08/34.93 powerset( 237.08/34.93 Y0), 237.08/34.93 powerset( 237.08/34.93 Y1))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 in( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1), 237.08/34.93 powerset( 237.08/34.93 Y0)))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 subset( 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))))))))) => 237.08/34.93 ((!!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))) => 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $o]: 237.08/34.93 (in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => Y3) => 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y1) => Y3) => 237.08/34.93 Y3))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) | 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 Y1, 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y2, Y0) => 237.08/34.93 (subset( 237.08/34.93 Y2, Y1) => 237.08/34.93 subset( 237.08/34.93 Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y0))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 Y1, Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 ~(( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 Y1))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y1, Y0) => 237.08/34.93 (binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1) = 237.08/34.93 Y0) => 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (binintersect( 237.08/34.93 Y0, 237.08/34.93 binunion( 237.08/34.93 Y1, Y2)) = 237.08/34.93 binunion( 237.08/34.93 binintersect( 237.08/34.93 Y0, Y1), 237.08/34.93 binintersect( 237.08/34.93 Y0, Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)) => 237.08/34.93 in(Y2, 237.08/34.93 Y0))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (subset( 237.08/34.93 Y0, Y1) => 237.08/34.93 (setminus( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))) => 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in(Y2, 237.08/34.93 Y1)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 Y0)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 setminus( 237.08/34.93 Y0, Y1)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 subset( 237.08/34.93 setminus( 237.08/34.93 Y0, Y1), 237.08/34.93 Y0))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (( 237.08/34.93 setminus( 237.08/34.93 Y0, Y1) = 237.08/34.93 emptyset) => 237.08/34.93 subset( 237.08/34.93 Y0, Y1)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $o]: 237.08/34.93 (( 237.08/34.93 in(Y2, 237.08/34.93 Y0) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 Y3)) => 237.08/34.93 (( 237.08/34.93 ( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 ( 237.08/34.93 in(Y2, 237.08/34.93 Y1) => Y3)) => 237.08/34.93 Y3))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (in(Y2, 237.08/34.93 Y1) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y0))) => 237.08/34.93 (( 237.08/34.93 ~( 237.08/34.93 in(Y2, 237.08/34.93 Y1))) => 237.08/34.93 (~( 237.08/34.93 in(Y2, 237.08/34.93 symdiff( 237.08/34.93 Y0, Y1))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)))) & 237.08/34.93 (setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)) = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 Y0)))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 Y0))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 setadjoin( 237.08/34.93 Y1, 237.08/34.93 emptyset))) => 237.08/34.93 (( 237.08/34.93 Y2 = Y1) | 237.08/34.93 (Y2 = Y0)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 subset( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 powerset( 237.08/34.93 powerset( 237.08/34.93 binunion( 237.08/34.93 Y0, Y1)))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y1) => 237.08/34.93 in( 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset)), 237.08/34.93 emptyset)), 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 Y1) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 cartprod( 237.08/34.93 Y0, Y1)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (??(( 237.08/34.93 ^[Y4 : $i]: 237.08/34.93 (in(Y4, 237.08/34.93 setunion( 237.08/34.93 Y2)) & 237.08/34.93 (Y2 = 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset), 237.08/34.93 setadjoin( 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 setadjoin( 237.08/34.93 Y4, 237.08/34.93 emptyset)), 237.08/34.93 emptyset))))))))))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i]: 237.08/34.93 (in(Y1, 237.08/34.93 setunion( 237.08/34.93 Y0)) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 in(Y1, 237.08/34.93 Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)), 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 subset( 237.08/34.93 Y0, 237.08/34.93 setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (setunion( 237.08/34.93 setadjoin( 237.08/34.93 Y0, 237.08/34.93 emptyset)) = 237.08/34.93 Y0)))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (!!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y2 = Y3))))))))))) => 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))))))))))) => 237.08/34.93 ( 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (( 237.08/34.93 ??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y2, 237.08/34.93 emptyset)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) & 237.08/34.93 Y1(Y2)))))))))))) => 237.08/34.93 ( 237.08/34.93 !!(( 237.08/34.93 ^[Y0 : $i]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y1 : $i > $o]: 237.08/34.93 (!!(( 237.08/34.93 ^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y2) => 237.08/34.93 (( 237.08/34.93 !!(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 Y0) => 237.08/34.93 (Y1(Y3) => 237.08/34.93 (Y3 = Y2)))))) => 237.08/34.93 (??(( 237.08/34.93 ^[Y3 : $i]: 237.08/34.93 (in(Y3, 237.08/34.93 dsetconstr( 237.08/34.93 Y0, Y1)) & 237.08/34.93 (dsetconstr( 237.08/34.93 Y0, Y1) = 237.08/34.93 setadjoin( 237.08/34.93 Y3, 237.08/34.93 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.93 inference('lazy_cnf_imply', [status(thm)], ['206'])). 237.08/34.93 tff('208', plain, 237.08/34.93 ~ ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y1, Y2) => 237.08/34.93 (in(Y2, Y0) => in(Y1, setunion(Y0))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, setunion(Y0)) => 237.08/34.93 (!!((^[Y2 : $o]: 237.08/34.93 ((!!((^[Y3 : $i]: 237.08/34.93 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.93 Y2))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 != Y1) => 237.08/34.93 (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.93 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, 237.08/34.93 setadjoin(Y0, 237.08/34.93 setadjoin(Y1, emptyset))) => 237.08/34.93 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i]: 237.08/34.93 in(Y1, 237.08/34.93 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.93 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.93 (~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.93 (~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i]: 237.08/34.93 (!!((^[Y1 : $i > $o]: 237.08/34.93 ((~((!!((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.93 (??((^[Y2 : $i]: 237.08/34.93 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.93 ((!!((^[Y0 : $i > $o]: 237.08/34.93 ((??(Y0)) => 237.08/34.93 ((!!((^[Y1 : $i]: 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y1) => 237.08/34.93 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.93 (??((^[Y1 : $i]: 237.08/34.93 (Y0(Y1) & 237.08/34.93 (!!((^[Y2 : $i]: 237.08/34.93 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.94 (??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) <=> 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y0(Y3) => 237.08/34.94 (Y2 = Y3))))))))) <=> 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (setadjoin( 237.08/34.94 Y0, Y2) = 237.08/34.94 setadjoin( 237.08/34.94 Y1, Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (powerset(Y0) = 237.08/34.94 powerset(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (setunion(Y0) = 237.08/34.94 setunion(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 Y2 = Y3) => 237.08/34.94 ( 237.08/34.94 Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y0(Y3) => 237.08/34.94 (Y2 = Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (Y1(Y3) => 237.08/34.94 ( 237.08/34.94 Y2 = Y3))))))))) => 237.08/34.94 (descr(Y0) = 237.08/34.94 descr(Y1))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i > $o]: 237.08/34.94 (!!((^[Y3 : $i > $o]: 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y5 : $i]: 237.08/34.94 (in(Y5, 237.08/34.94 Y1) => 237.08/34.94 (( 237.08/34.94 Y4 = Y5) => 237.08/34.94 (Y2(Y4) <=> 237.08/34.94 Y3(Y5))))))))))) => 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y2) = 237.08/34.94 dsetconstr( 237.08/34.94 Y1, Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!(subset(emptyset))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 ( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((~(subset( 237.08/34.94 Y0, Y1))) => 237.08/34.94 (Y0 != Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 Y0 != Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 subset(Y0, Y0)))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (subset( 237.08/34.94 Y1, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 (Y0 = Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (subset(Y0, 237.08/34.94 emptyset) => 237.08/34.94 (Y0 = 237.08/34.94 emptyset))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0)) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y0))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 subset( 237.08/34.94 powerset( 237.08/34.94 Y0), 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 in( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 powerset( 237.08/34.94 Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 subset( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => Y3) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) | 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y1, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y2, Y0) => 237.08/34.94 (subset( 237.08/34.94 Y2, Y1) => 237.08/34.94 subset( 237.08/34.94 Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 ~(( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y1))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (binintersect( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y1, Y2)) = 237.08/34.94 binunion( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 binintersect( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 Y1)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 Y3)) => 237.08/34.94 (( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 ( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3)) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)) = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)) = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 Y0) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset), 237.08/34.94 Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 Y0) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset), 237.08/34.94 powerset( 237.08/34.94 Y0))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))) => 237.08/34.94 (( 237.08/34.94 Y2 = Y1) | 237.08/34.94 (Y2 = Y0)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) & 237.08/34.94 (??(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 Y1) & 237.08/34.94 (Y2 = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 setadjoin( 237.08/34.94 Y4, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 Y2)) & 237.08/34.94 (??(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 setunion( 237.08/34.94 Y2)) & 237.08/34.94 (Y2 = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 setadjoin( 237.08/34.94 Y4, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 setunion( 237.08/34.94 Y0)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 in(Y1, 237.08/34.94 Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 subset( 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)), 237.08/34.94 Y0)))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)) = 237.08/34.94 Y0)))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y2) => 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))))) => 237.08/34.94 (( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 Y1(Y2))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset)))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 Y1(Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y2) => 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y3 = Y2)))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.94 inference('lazy_cnf_imply', [status(thm)], ['207'])). 237.08/34.94 tff('209', plain, 237.08/34.94 ~ ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y1, setunion(Y0)) => 237.08/34.94 (!!((^[Y2 : $o]: 237.08/34.94 ((!!((^[Y3 : $i]: 237.08/34.94 (in(Y1, Y3) => (in(Y3, Y0) => Y2))))) => 237.08/34.94 Y2))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.94 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.08/34.94 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.94 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.94 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.94 (~((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.94 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??(Y0)) => 237.08/34.94 ((!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.94 (??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) <=> 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y0(Y3) => 237.08/34.94 (Y2 = Y3))))))))) <=> 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (setadjoin( 237.08/34.94 Y0, Y2) = 237.08/34.94 setadjoin( 237.08/34.94 Y1, Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (powerset(Y0) = 237.08/34.94 powerset(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (setunion(Y0) = 237.08/34.94 setunion(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (( 237.08/34.94 Y2 = Y3) => 237.08/34.94 ( 237.08/34.94 Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y0(Y3) => 237.08/34.94 (Y2 = Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))) => 237.08/34.94 (descr(Y0) = descr(Y1))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i > $o]: 237.08/34.94 (!!((^[Y3 : $i > $o]: 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y5 : $i]: 237.08/34.94 (in(Y5, 237.08/34.94 Y1) => 237.08/34.94 (( 237.08/34.94 Y4 = Y5) => 237.08/34.94 (Y2(Y4) <=> 237.08/34.94 Y3(Y5))))))))))) => 237.08/34.94 ( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y2) = 237.08/34.94 dsetconstr( 237.08/34.94 Y1, Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!(subset(emptyset))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 ( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((~(subset(Y0, 237.08/34.94 Y1))) => 237.08/34.94 (Y0 != Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (Y0 != Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 subset(Y0, Y0)))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y1, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 subset(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 (Y0 = Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (subset(Y0, 237.08/34.94 emptyset) => 237.08/34.94 (Y0 = 237.08/34.94 emptyset))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 ( 237.08/34.94 in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0)) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y0))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 subset( 237.08/34.94 powerset( 237.08/34.94 Y0), 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 in( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 powerset( 237.08/34.94 Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 subset( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => Y3) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) | 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))) => 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y1, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y2, Y0) => 237.08/34.94 (subset( 237.08/34.94 Y2, Y1) => 237.08/34.94 subset( 237.08/34.94 Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 ~(( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y1))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (binintersect( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y1, Y2)) = 237.08/34.94 binunion( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 binintersect( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 Y1)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 Y3)) => 237.08/34.94 (( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 ( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3)) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)) = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)) = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 Y0) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset), 237.08/34.94 Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 Y0) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset), 237.08/34.94 powerset( 237.08/34.94 Y0))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))) => 237.08/34.94 (( 237.08/34.94 Y2 = Y1) | 237.08/34.94 (Y2 = Y0)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) & 237.08/34.94 (??(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 Y1) & 237.08/34.94 (Y2 = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 setadjoin( 237.08/34.94 Y4, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 Y2)) & 237.08/34.94 (??(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 setunion( 237.08/34.94 Y2)) & 237.08/34.94 (Y2 = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 setadjoin( 237.08/34.94 Y4, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 setunion( 237.08/34.94 Y0)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 in(Y1, 237.08/34.94 Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 subset( 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)), 237.08/34.94 Y0)))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)) = 237.08/34.94 Y0)))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y2) => 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))))) => 237.08/34.94 (( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 Y1(Y2))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset)))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 Y1(Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y2) => 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y3 = Y2)))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.94 inference('lazy_cnf_imply', [status(thm)], ['208'])). 237.08/34.94 tff('210', plain, 237.08/34.94 ~ ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: (in(Y1, Y0) => in(Y1, powerset(setunion(Y0)))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.94 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.08/34.94 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.94 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.94 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.94 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.94 (~((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.94 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??(Y0)) => 237.08/34.94 ((!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.94 (??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) <=> 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y0(Y3) => 237.08/34.94 (Y2 = Y3))))))))) <=> 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (setadjoin( 237.08/34.94 Y0, Y2) = 237.08/34.94 setadjoin( 237.08/34.94 Y1, Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (powerset(Y0) = powerset(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (setunion(Y0) = 237.08/34.94 setunion(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ( 237.08/34.94 Y0(Y3) => 237.08/34.94 ( 237.08/34.94 Y2 = Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))) => 237.08/34.94 (descr(Y0) = descr(Y1))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i > $o]: 237.08/34.94 (!!((^[Y3 : $i > $o]: 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y5 : $i]: 237.08/34.94 (in(Y5, 237.08/34.94 Y1) => 237.08/34.94 (( 237.08/34.94 Y4 = Y5) => 237.08/34.94 (Y2(Y4) <=> 237.08/34.94 Y3(Y5))))))))))) => 237.08/34.94 ( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y2) = 237.08/34.94 dsetconstr( 237.08/34.94 Y1, Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!(subset(emptyset))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset(Y0, 237.08/34.94 Y1) => 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((~(subset(Y0, 237.08/34.94 Y1))) => 237.08/34.94 (Y0 != Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (Y0 != Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 subset(Y0, Y0)))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y1, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 subset(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 ( 237.08/34.94 Y0 = Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (subset(Y0, 237.08/34.94 emptyset) => 237.08/34.94 (Y0 = emptyset))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0)) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y0))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 subset( 237.08/34.94 powerset( 237.08/34.94 Y0), 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 in( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 powerset( 237.08/34.94 Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 subset( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => Y3) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) | 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y1, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y2, Y0) => 237.08/34.94 (subset( 237.08/34.94 Y2, Y1) => 237.08/34.94 subset( 237.08/34.94 Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 ~(( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y1))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (binintersect( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y1, Y2)) = 237.08/34.94 binunion( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 binintersect( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 Y1)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 Y3)) => 237.08/34.94 (( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 ( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3)) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)) = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)) = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 Y0) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset), 237.08/34.94 Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 Y0) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset), 237.08/34.94 powerset( 237.08/34.94 Y0))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))) => 237.08/34.94 (( 237.08/34.94 Y2 = Y1) | 237.08/34.94 (Y2 = Y0)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 powerset( 237.08/34.94 powerset( 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y1) => 237.08/34.94 in( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)), 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) & 237.08/34.94 (??(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 Y1) & 237.08/34.94 (Y2 = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 setadjoin( 237.08/34.94 Y4, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 cartprod( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 Y2)) & 237.08/34.94 (??(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 setunion( 237.08/34.94 Y2)) & 237.08/34.94 (Y2 = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 setadjoin( 237.08/34.94 Y4, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 setunion( 237.08/34.94 Y0)) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 in(Y1, 237.08/34.94 Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 subset( 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)), 237.08/34.94 Y0)))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (setunion( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset)) = 237.08/34.94 Y0)))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y2) => 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))))) => 237.08/34.94 (( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 Y1(Y2))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset)))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 Y1(Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y2) => 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 Y0) => 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y3 = Y2)))))) => 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1)) & 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y1) = 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.08/34.94 inference('lazy_cnf_imply', [status(thm)], ['209'])). 237.08/34.94 tff('211', plain, 237.08/34.94 ~ ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y0, setadjoin(Y1, emptyset)) => 237.08/34.94 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.08/34.94 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.08/34.94 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.94 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.08/34.94 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.08/34.94 (~((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.08/34.94 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & Y1(Y2))))))) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((~((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => Y1(Y2))))))) => 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??(Y0)) => 237.08/34.94 ((!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.08/34.94 (??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (in(Y2, Y0) <=> 237.08/34.94 in(Y3, Y1)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y0(Y3) => 237.08/34.94 (Y2 = Y3))))))))) <=> 237.08/34.94 (??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y1(Y3) => 237.08/34.94 (Y2 = Y3))))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (setadjoin(Y0, 237.08/34.94 Y2) = 237.08/34.94 setadjoin(Y1, 237.08/34.94 Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (powerset(Y0) = powerset(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (setunion(Y0) = setunion(Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 ((??((^[Y1 : $i]: 237.08/34.94 (Y0(Y1) & 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))) => 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (Y0(Y1) => 237.08/34.94 (Y0(Y2) => 237.08/34.94 (Y1 = Y2))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i > $o]: 237.08/34.94 (!!((^[Y1 : $i > $o]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ((Y2 = Y3) => 237.08/34.94 (Y0(Y2) <=> 237.08/34.94 Y1(Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y0(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 (Y0(Y3) => 237.08/34.94 ( 237.08/34.94 Y2 = Y3))))))))) => 237.08/34.94 ((??((^[Y2 : $i]: 237.08/34.94 (Y1(Y2) & 237.08/34.94 (!!((^[Y3 : $i]: 237.08/34.94 ( 237.08/34.94 Y1(Y3) => 237.08/34.94 ( 237.08/34.94 Y2 = Y3))))))))) => 237.08/34.94 (descr(Y0) = descr(Y1))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 (!!((^[Y2 : $i > $o]: 237.08/34.94 (!!((^[Y3 : $i > $o]: 237.08/34.94 ((!!(( 237.08/34.94 ^[Y4 : $i]: 237.08/34.94 (in(Y4, 237.08/34.94 Y0) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y5 : $i]: 237.08/34.94 (in(Y5, 237.08/34.94 Y1) => 237.08/34.94 (( 237.08/34.94 Y4 = Y5) => 237.08/34.94 (Y2(Y4) <=> 237.08/34.94 Y3(Y5))))))))))) => 237.08/34.94 (dsetconstr( 237.08/34.94 Y0, Y2) = 237.08/34.94 dsetconstr( 237.08/34.94 Y1, Y3)))))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((Y0 = Y1) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1))))) => 237.08/34.94 subset(Y0, Y1)))))))) => 237.08/34.94 ((!!(subset(emptyset))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset(Y0, 237.08/34.94 Y1) => 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 in(Y2, Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset(Y0, 237.08/34.94 Y1) => 237.08/34.94 ((~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (in(Y2, Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 ((~(subset(Y0, 237.08/34.94 Y1))) => 237.08/34.94 (Y0 != Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 ( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 ( 237.08/34.94 Y0 != Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 subset(Y0, Y0)))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!((^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (subset( 237.08/34.94 Y1, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 subset(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y0, Y2) => 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, Y2)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 ( 237.08/34.94 Y0 = Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (subset(Y0, 237.08/34.94 emptyset) => 237.08/34.94 (Y0 = emptyset))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!((^[Y1 : $i]: 237.08/34.94 (in(Y1, 237.08/34.94 powerset( 237.08/34.94 Y0)) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 powerset( 237.08/34.94 Y0))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 ( 237.08/34.94 subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 subset( 237.08/34.94 powerset( 237.08/34.94 Y0), 237.08/34.94 powerset( 237.08/34.94 Y1))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 in( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 powerset( 237.08/34.94 Y0)))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i > $o]: 237.08/34.94 subset( 237.08/34.94 dsetconstr( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ((!!((^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => Y3) => 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) | 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ((!!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 Y1, 237.08/34.94 binunion( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 (( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y2, Y0) => 237.08/34.94 (subset( 237.08/34.94 Y2, Y1) => 237.08/34.94 subset( 237.08/34.94 Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1) => 237.08/34.94 subset( 237.08/34.94 Y1, Y0)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 ~(( 237.08/34.94 ??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) & 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 Y1))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y1, Y0) => 237.08/34.94 (binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1) = 237.08/34.94 Y0) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (binintersect( 237.08/34.94 Y0, 237.08/34.94 binunion( 237.08/34.94 Y1, Y2)) = 237.08/34.94 binunion( 237.08/34.94 binintersect( 237.08/34.94 Y0, Y1), 237.08/34.94 binintersect( 237.08/34.94 Y0, Y2)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 in(Y2, 237.08/34.94 Y0))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (subset( 237.08/34.94 Y0, Y1) => 237.08/34.94 (setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 in(Y2, 237.08/34.94 Y1)))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 Y0)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 setminus( 237.08/34.94 Y0, Y1)))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 subset( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1), 237.08/34.94 Y0))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (( 237.08/34.94 setminus( 237.08/34.94 Y0, Y1) = 237.08/34.94 emptyset) => 237.08/34.94 subset( 237.08/34.94 Y0, Y1)))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1)) => 237.08/34.94 (!!(( 237.08/34.94 ^[Y3 : $o]: 237.08/34.94 (( 237.08/34.94 in(Y2, 237.08/34.94 Y0) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 Y3)) => 237.08/34.94 (( 237.08/34.94 ( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 ( 237.08/34.94 in(Y2, 237.08/34.94 Y1) => Y3)) => 237.08/34.94 Y3))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 Y0) => 237.08/34.94 (in(Y2, 237.08/34.94 Y1) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y0))) => 237.08/34.94 (( 237.08/34.94 ~( 237.08/34.94 in(Y2, 237.08/34.94 Y1))) => 237.08/34.94 (~( 237.08/34.94 in(Y2, 237.08/34.94 symdiff( 237.08/34.94 Y0, Y1))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y0, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 in(Y1, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)) = 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y2, 237.08/34.94 setadjoin( 237.08/34.94 Y3, 237.08/34.94 emptyset)), 237.08/34.94 emptyset))))))))))))))))) => 237.08/34.94 ( 237.08/34.94 ( 237.08/34.94 !!(( 237.08/34.94 ^[Y0 : $i]: 237.08/34.94 (!!(( 237.08/34.94 ^[Y1 : $i]: 237.08/34.94 (??(( 237.08/34.94 ^[Y2 : $i]: 237.08/34.94 (in(Y2, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (??(( 237.08/34.94 ^[Y3 : $i]: 237.08/34.94 (in(Y3, 237.08/34.94 setunion( 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.94 Y1, 237.08/34.94 emptyset)), 237.08/34.94 emptyset)))) & 237.08/34.94 (setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 emptyset), 237.08/34.94 setadjoin( 237.08/34.94 setadjoin( 237.08/34.94 Y0, 237.08/34.94 setadjoin( 237.08/34.95 Y1, 237.08/34.95 emptyset)), 237.08/34.95 emptyset)) = 237.08/34.95 setadjoin( 237.08/34.95 setadjoin( 237.08/34.95 Y2, 237.08/34.95 emptyset), 237.08/34.95 setadjoin( 237.08/34.95 setadjoin( 237.08/34.95 Y2, 237.08/34.95 setadjoin( 237.08/34.95 Y3, 237.08/34.95 emptyset)), 237.08/34.95 emptyset))))))))))))))))) => 237.08/34.95 ( 237.08/34.95 ( 237.08/34.95 !!(( 237.08/34.95 ^[Y0 : $i]: 237.08/34.95 (!!(( 237.08/34.95 ^[Y1 : $i]: 237.08/34.95 (in(Y1, 237.08/34.95 Y0) => 237.08/34.95 subset( 237.08/34.95 setadjoin( 237.08/34.95 Y1, 237.08/34.95 emptyset), 237.08/34.95 Y0)))))))) => 237.08/34.95 ( 237.08/34.95 ( 237.08/34.95 !!(( 237.08/34.95 ^[Y0 : $i]: 237.08/34.95 (!!(( 237.08/34.95 ^[Y1 : $i]: 237.08/34.95 (in(Y1, 237.08/34.95 Y0) => 237.08/34.95 in( 237.08/34.95 setadjoin( 237.08/34.95 Y1, 237.08/34.95 emptyset), 237.08/34.95 powerset( 237.08/34.95 Y0))))))))) => 237.08/34.95 ( 237.08/34.95 ( 237.08/34.95 !!(( 237.08/34.95 ^[Y0 : $i]: 237.08/34.95 (!!(( 237.08/34.95 ^[Y1 : $i]: 237.08/34.95 (!!(( 237.08/34.95 ^[Y2 : $i]: 237.08/34.95 (in(Y2, 237.08/34.95 Y0) => 237.08/34.95 in( 237.08/34.95 setadjoin( 237.08/34.95 Y2, 237.08/34.95 emptyset), 237.08/34.95 powerset( 237.08/34.95 binunion( 237.08/34.95 Y0, Y1))))))))))))) => 237.08/34.95 ( 237.08/34.95 ( 237.08/34.95 !!(( 237.08/34.95 ^[Y0 : $i]: 237.08/34.95 (!!(( 237.08/34.95 ^[Y1 : $i]: 237.08/34.95 (!!(( 237.08/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))) => 237.26/34.95 (( 237.26/34.95 Y2 = Y1) | 237.26/34.95 (Y2 = Y0)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 Y1) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 setunion( 237.26/34.95 Y0)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y1, 237.26/34.95 Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)), 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)) = 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))) => 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y3 = Y2)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.95 inference('lazy_cnf_imply', [status(thm)], ['210'])). 237.26/34.95 tff('212', plain, 237.26/34.95 ~ ((!!((^[Y0 : $i]: ((Y0 != emptyset) => (??((^[Y1 : $i]: in(Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y0, setadjoin(Y1, emptyset)) => 237.26/34.95 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.26/34.95 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.95 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.95 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.95 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??(Y0)) => 237.26/34.95 ((!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) <=> 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> 237.26/34.95 Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) <=> 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (setadjoin(Y0, 237.26/34.95 Y2) = 237.26/34.95 setadjoin(Y1, 237.26/34.95 Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> 237.26/34.95 Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 ( 237.26/34.95 Y2 = Y3))))))))) => 237.26/34.95 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i > $o]: 237.26/34.95 (!!((^[Y3 : $i > $o]: 237.26/34.95 ((!!(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y5 : $i]: 237.26/34.95 (in(Y5, 237.26/34.95 Y1) => 237.26/34.95 (( 237.26/34.95 Y4 = Y5) => 237.26/34.95 (Y2(Y4) <=> 237.26/34.95 Y3(Y5))))))))))) => 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y2) = 237.26/34.95 dsetconstr( 237.26/34.95 Y1, Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 subset(Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!(subset(emptyset))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 ((~( 237.26/34.95 in(Y2, Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, Y0)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 ((~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((~(subset(Y0, Y1))) => 237.26/34.95 (Y0 != Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 ( 237.26/34.95 Y0 != Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 subset(Y0, Y0)))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (subset( 237.26/34.95 Y1, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 subset(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 in(Y0, 237.26/34.95 powerset( 237.26/34.95 Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 ( 237.26/34.95 Y0 = Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 emptyset) => 237.26/34.95 (Y0 = emptyset))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ( 237.26/34.95 subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0)) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 in(Y0, 237.26/34.95 powerset(Y0))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 subset( 237.26/34.95 powerset( 237.26/34.95 Y0), 237.26/34.95 powerset( 237.26/34.95 Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 in( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 powerset( 237.26/34.95 Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 subset( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y0) => Y3) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y1) => Y3) => 237.26/34.95 Y3))))))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) | 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y1, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y2, Y0) => 237.26/34.95 (subset( 237.26/34.95 Y2, Y1) => 237.26/34.95 subset( 237.26/34.95 Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 ~(( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y1))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (binintersect( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y1, Y2)) = 237.26/34.95 binunion( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 binintersect( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 Y1)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y0) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 Y3)) => 237.26/34.95 (( 237.26/34.95 ( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 ( 237.26/34.95 in(Y2, 237.26/34.95 Y1) => Y3)) => 237.26/34.95 Y3))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y0, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)) = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)) = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 Y0) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset), 237.26/34.95 Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 Y0) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset), 237.26/34.95 powerset( 237.26/34.95 Y0))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))) => 237.26/34.95 (( 237.26/34.95 Y2 = Y1) | 237.26/34.95 (Y2 = Y0)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 Y1) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 setunion( 237.26/34.95 Y0)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y1, 237.26/34.95 Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)), 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)) = 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))) => 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y3 = Y2)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.95 inference('lazy_cnf_imply', [status(thm)], ['211'])). 237.26/34.95 tff('213', plain, 237.26/34.95 ~ ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: (in(Y0, setadjoin(Y1, emptyset)) => (Y0 = Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y0, setadjoin(Y1, emptyset)) => 237.26/34.95 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.26/34.95 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.95 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.95 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.95 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??(Y0)) => 237.26/34.95 ((!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) <=> 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) <=> 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (setadjoin(Y0, 237.26/34.95 Y2) = 237.26/34.95 setadjoin(Y1, 237.26/34.95 Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> 237.26/34.95 Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))) => 237.26/34.95 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i > $o]: 237.26/34.95 (!!((^[Y3 : $i > $o]: 237.26/34.95 ((!!(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 ( 237.26/34.95 in(Y4, 237.26/34.95 Y0) => 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y5 : $i]: 237.26/34.95 (in(Y5, 237.26/34.95 Y1) => 237.26/34.95 (( 237.26/34.95 Y4 = Y5) => 237.26/34.95 (Y2(Y4) <=> 237.26/34.95 Y3(Y5))))))))))) => 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y2) = 237.26/34.95 dsetconstr( 237.26/34.95 Y1, Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 subset(Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!(subset(emptyset))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, Y1) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 ((~(in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~(in(Y2, 237.26/34.95 Y0)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 ((~( 237.26/34.95 in(Y2, Y1))) => 237.26/34.95 (~( 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((~(subset(Y0, Y1))) => 237.26/34.95 (Y0 != Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 ( 237.26/34.95 Y0 != Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 ( 237.26/34.95 subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 ( 237.26/34.95 subset( 237.26/34.95 Y1, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 subset(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 in(Y0, 237.26/34.95 powerset( 237.26/34.95 Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 (Y0 = Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 emptyset) => 237.26/34.95 (Y0 = emptyset))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ( 237.26/34.95 in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0)) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 in(Y0, 237.26/34.95 powerset(Y0))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 subset( 237.26/34.95 powerset( 237.26/34.95 Y0), 237.26/34.95 powerset( 237.26/34.95 Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 in( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 powerset( 237.26/34.95 Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 subset( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y0) => Y3) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y1) => Y3) => 237.26/34.95 Y3))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) | 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y1, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y2, Y0) => 237.26/34.95 (subset( 237.26/34.95 Y2, Y1) => 237.26/34.95 subset( 237.26/34.95 Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 ~(( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y1))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (binintersect( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y1, Y2)) = 237.26/34.95 binunion( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 binintersect( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 Y1)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y0) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 Y3)) => 237.26/34.95 (( 237.26/34.95 ( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 ( 237.26/34.95 in(Y2, 237.26/34.95 Y1) => Y3)) => 237.26/34.95 Y3))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y0, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)) = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)) = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 Y0) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset), 237.26/34.95 Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 Y0) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset), 237.26/34.95 powerset( 237.26/34.95 Y0))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))) => 237.26/34.95 (( 237.26/34.95 Y2 = Y1) | 237.26/34.95 (Y2 = Y0)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 Y1) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 setunion( 237.26/34.95 Y0)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y1, 237.26/34.95 Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)), 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)) = 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))) => 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y3 = Y2)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.95 inference('lazy_cnf_imply', [status(thm)], ['212'])). 237.26/34.95 tff('214', plain, 237.26/34.95 ~ ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 != Y1) => (~(in(Y1, setadjoin(Y0, emptyset))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y0, setadjoin(Y1, emptyset)) => 237.26/34.95 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.26/34.95 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.95 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.95 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.95 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??(Y0)) => 237.26/34.95 ((!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) <=> 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) <=> 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (setadjoin(Y0, Y2) = 237.26/34.95 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> 237.26/34.95 Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))) => 237.26/34.95 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i > $o]: 237.26/34.95 (!!((^[Y3 : $i > $o]: 237.26/34.95 ((!!(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 Y0) => 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y5 : $i]: 237.26/34.95 (in(Y5, 237.26/34.95 Y1) => 237.26/34.95 (( 237.26/34.95 Y4 = Y5) => 237.26/34.95 (Y2(Y4) <=> 237.26/34.95 Y3(Y5))))))))))) => 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y2) = 237.26/34.95 dsetconstr( 237.26/34.95 Y1, Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 subset(Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!(subset(emptyset))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, Y1) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, Y1) => 237.26/34.95 ((~(in(Y2, Y1))) => 237.26/34.95 (~(in(Y2, Y0)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 ((~(in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~(subset( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((~(subset(Y0, Y1))) => 237.26/34.95 (Y0 != Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 ((~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (Y0 != Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 ( 237.26/34.95 subset( 237.26/34.95 Y1, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 subset(Y1, 237.26/34.95 setadjoin(Y0, 237.26/34.95 Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 in(Y0, 237.26/34.95 powerset( 237.26/34.95 Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 (subset(Y1, 237.26/34.95 Y0) => 237.26/34.95 (Y0 = Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 emptyset) => 237.26/34.95 (Y0 = emptyset))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0)) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 in(Y0, 237.26/34.95 powerset(Y0))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 subset( 237.26/34.95 powerset( 237.26/34.95 Y0), 237.26/34.95 powerset( 237.26/34.95 Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 in( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 powerset( 237.26/34.95 Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 subset( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y0) => Y3) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y1) => Y3) => 237.26/34.95 Y3))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) | 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y1, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y2, Y0) => 237.26/34.95 (subset( 237.26/34.95 Y2, Y1) => 237.26/34.95 subset( 237.26/34.95 Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 ~(( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y1))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (binintersect( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y1, Y2)) = 237.26/34.95 binunion( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 binintersect( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 Y1)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y0) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 Y3)) => 237.26/34.95 (( 237.26/34.95 ( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 ( 237.26/34.95 in(Y2, 237.26/34.95 Y1) => Y3)) => 237.26/34.95 Y3))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y0, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)) = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)))) & 237.26/34.95 (setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)) = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 Y0) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset), 237.26/34.95 Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 Y0) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset), 237.26/34.95 powerset( 237.26/34.95 Y0))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))) => 237.26/34.95 (( 237.26/34.95 Y2 = Y1) | 237.26/34.95 (Y2 = Y0)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 powerset( 237.26/34.95 powerset( 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y1) => 237.26/34.95 in( 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)), 237.26/34.95 emptyset)), 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 Y1) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 cartprod( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (??(( 237.26/34.95 ^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 setunion( 237.26/34.95 Y2)) & 237.26/34.95 (Y2 = 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset), 237.26/34.95 setadjoin( 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 setadjoin( 237.26/34.95 Y4, 237.26/34.95 emptyset)), 237.26/34.95 emptyset))))))))))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 setunion( 237.26/34.95 Y0)) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y1, 237.26/34.95 Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)), 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (setunion( 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 emptyset)) = 237.26/34.95 Y0)))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))) => 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y2, 237.26/34.95 emptyset)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 Y1(Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i > $o]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y2) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 Y0) => 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y3 = Y2)))))) => 237.26/34.95 (??(( 237.26/34.95 ^[Y3 : $i]: 237.26/34.95 (in(Y3, 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1)) & 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y1) = 237.26/34.95 setadjoin( 237.26/34.95 Y3, 237.26/34.95 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.95 inference('lazy_cnf_imply', [status(thm)], ['213'])). 237.26/34.95 tff('215', plain, 237.26/34.95 ~ ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: ((Y0 = Y1) => in(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y0, setadjoin(Y1, emptyset)) => 237.26/34.95 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.26/34.95 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.95 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.95 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.95 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((~((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??(Y0)) => 237.26/34.95 ((!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.95 (??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (in(Y2, Y0) <=> 237.26/34.95 in(Y3, Y1)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) <=> 237.26/34.95 (??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (setadjoin(Y0, Y2) = 237.26/34.95 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 ((??((^[Y1 : $i]: 237.26/34.95 (Y0(Y1) & 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (Y0(Y1) => 237.26/34.95 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i > $o]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 ((Y2 = Y3) => 237.26/34.95 (Y0(Y2) <=> 237.26/34.95 Y1(Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y0(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y0(Y3) => 237.26/34.95 (Y2 = Y3))))))))) => 237.26/34.95 ((??((^[Y2 : $i]: 237.26/34.95 (Y1(Y2) & 237.26/34.95 (!!((^[Y3 : $i]: 237.26/34.95 (Y1(Y3) => 237.26/34.95 (Y2 = Y3))))))))) => 237.26/34.95 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 (!!((^[Y2 : $i > $o]: 237.26/34.95 (!!((^[Y3 : $i > $o]: 237.26/34.95 ((!!((^[Y4 : $i]: 237.26/34.95 (in(Y4, 237.26/34.95 Y0) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y5 : $i]: 237.26/34.95 (in(Y5, 237.26/34.95 Y1) => 237.26/34.95 (( 237.26/34.95 Y4 = Y5) => 237.26/34.95 (Y2(Y4) <=> 237.26/34.95 Y3(Y5))))))))))) => 237.26/34.95 (dsetconstr( 237.26/34.95 Y0, Y2) = 237.26/34.95 dsetconstr( 237.26/34.95 Y1, Y3)))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((Y0 = Y1) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1))))) => 237.26/34.95 subset(Y0, Y1)))))))) => 237.26/34.95 ((!!(subset(emptyset))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, Y1) => 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 in(Y2, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset(Y0, Y1) => 237.26/34.95 ((~(in(Y2, Y1))) => 237.26/34.95 (~(in(Y2, Y0)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 ((~(in(Y2, Y1))) => 237.26/34.95 (~(subset( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ((~(subset(Y0, Y1))) => 237.26/34.95 (Y0 != Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (in(Y2, Y0) => 237.26/34.95 ((~( 237.26/34.95 in(Y2, Y1))) => 237.26/34.95 (Y0 != Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (subset( 237.26/34.95 Y1, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 subset(Y1, 237.26/34.95 setadjoin(Y0, 237.26/34.95 Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (!!((^[Y2 : $i]: 237.26/34.95 ( 237.26/34.95 subset( 237.26/34.95 Y0, Y2) => 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, Y2)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y0, Y1) => 237.26/34.95 in(Y0, 237.26/34.95 powerset(Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 Y1) => 237.26/34.95 (subset(Y1, 237.26/34.95 Y0) => 237.26/34.95 (Y0 = Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (subset(Y0, 237.26/34.95 emptyset) => 237.26/34.95 (Y0 = emptyset))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (subset(Y1, 237.26/34.95 Y0) => 237.26/34.95 in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 (in(Y1, 237.26/34.95 powerset( 237.26/34.95 Y0)) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 in(Y0, 237.26/34.95 powerset(Y0))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i]: 237.26/34.95 ( 237.26/34.95 subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 subset( 237.26/34.95 powerset( 237.26/34.95 Y0), 237.26/34.95 powerset( 237.26/34.95 Y1))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 in( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 powerset( 237.26/34.95 Y0)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!((^[Y1 : $i > $o]: 237.26/34.95 subset( 237.26/34.95 dsetconstr( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 in(Y1, 237.26/34.95 setadjoin( 237.26/34.95 Y0, 237.26/34.95 setadjoin( 237.26/34.95 Y1, 237.26/34.95 emptyset))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y0) => Y3) => 237.26/34.95 (( 237.26/34.95 in(Y2, 237.26/34.95 Y1) => Y3) => 237.26/34.95 Y3))))))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) | 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!((^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 Y1, 237.26/34.95 binunion( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y2, Y0) => 237.26/34.95 (subset( 237.26/34.95 Y2, Y1) => 237.26/34.95 subset( 237.26/34.95 Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 ((!!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 (( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1) => 237.26/34.95 subset( 237.26/34.95 Y1, Y0)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 ~(( 237.26/34.95 ??(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) & 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 Y1))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y1, Y0) => 237.26/34.95 (binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1) = 237.26/34.95 Y0) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (binintersect( 237.26/34.95 Y0, 237.26/34.95 binunion( 237.26/34.95 Y1, Y2)) = 237.26/34.95 binunion( 237.26/34.95 binintersect( 237.26/34.95 Y0, Y1), 237.26/34.95 binintersect( 237.26/34.95 Y0, Y2)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 in(Y2, 237.26/34.95 Y0))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (subset( 237.26/34.95 Y0, Y1) => 237.26/34.95 (setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (in(Y2, 237.26/34.95 Y0) => 237.26/34.95 in(Y2, 237.26/34.95 Y1)))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))) => 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y1))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 Y0)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (( 237.26/34.95 ~( 237.26/34.95 in(Y2, 237.26/34.95 Y0))) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 Y1) => 237.26/34.95 (~( 237.26/34.95 in(Y2, 237.26/34.95 setminus( 237.26/34.95 Y0, Y1)))))))))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 subset( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1), 237.26/34.95 Y0))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (( 237.26/34.95 setminus( 237.26/34.95 Y0, Y1) = 237.26/34.95 emptyset) => 237.26/34.95 subset( 237.26/34.95 Y0, Y1)))))))) => 237.26/34.95 ( 237.26/34.95 ( 237.26/34.95 !!(( 237.26/34.95 ^[Y0 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y1 : $i]: 237.26/34.95 (!!(( 237.26/34.95 ^[Y2 : $i]: 237.26/34.95 (in(Y2, 237.26/34.95 symdiff( 237.26/34.95 Y0, Y1)) => 237.26/34.95 (!!(( 237.26/34.95 ^[Y3 : $o]: 237.26/34.95 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 Y3)) => 237.26/34.96 (( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 ( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3)) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 Y0)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 Y0))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))) => 237.26/34.96 (( 237.26/34.96 Y2 = Y1) | 237.26/34.96 (Y2 = Y0)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 Y1) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 setunion( 237.26/34.96 Y0)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y1, 237.26/34.96 Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)), 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)) = 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))))) => 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y3 = Y2)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.96 inference('lazy_cnf_imply', [status(thm)], ['214'])). 237.26/34.96 tff('216', plain, 237.26/34.96 ~ ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (in(Y0, setadjoin(Y1, emptyset)) => 237.26/34.96 in(Y1, setadjoin(Y0, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.26/34.96 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.96 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.96 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.96 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??(Y0)) => 237.26/34.96 ((!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) <=> 237.26/34.96 in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.96 (??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (setadjoin(Y0, Y2) = 237.26/34.96 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> 237.26/34.96 Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i > $o]: 237.26/34.96 (!!((^[Y3 : $i > $o]: 237.26/34.96 ((!!((^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y5 : $i]: 237.26/34.96 (in(Y5, 237.26/34.96 Y1) => 237.26/34.96 (( 237.26/34.96 Y4 = Y5) => 237.26/34.96 (Y2(Y4) <=> 237.26/34.96 Y3(Y5))))))))))) => 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y2) = 237.26/34.96 dsetconstr( 237.26/34.96 Y1, Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!(subset(emptyset))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(in(Y2, Y0)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(subset(Y0, 237.26/34.96 Y1)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((~(subset(Y0, Y1))) => 237.26/34.96 (Y0 != Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (Y0 != Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, 237.26/34.96 Y1) => 237.26/34.96 (subset( 237.26/34.96 Y1, Y2) => 237.26/34.96 subset( 237.26/34.96 Y0, Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 subset(Y1, 237.26/34.96 setadjoin(Y0, 237.26/34.96 Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y2) => 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 in(Y0, 237.26/34.96 powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (subset(Y1, 237.26/34.96 Y0) => 237.26/34.96 (Y0 = Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (subset(Y0, emptyset) => 237.26/34.96 (Y0 = emptyset))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y1, 237.26/34.96 Y0) => 237.26/34.96 in(Y1, 237.26/34.96 powerset( 237.26/34.96 Y0))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 powerset( 237.26/34.96 Y0)) => 237.26/34.96 subset(Y1, 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 in(Y0, 237.26/34.96 powerset(Y0))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 subset( 237.26/34.96 powerset( 237.26/34.96 Y0), 237.26/34.96 powerset( 237.26/34.96 Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 in( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 powerset( 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 subset( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => Y3) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) | 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y1, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y2, Y0) => 237.26/34.96 (subset( 237.26/34.96 Y2, Y1) => 237.26/34.96 subset( 237.26/34.96 Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0)))))))) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 Y1, Y0)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 ~(( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y1))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y1, Y0) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (binintersect( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y1, Y2)) = 237.26/34.96 binunion( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 binintersect( 237.26/34.96 Y0, Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 Y1)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 Y3)) => 237.26/34.96 (( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 ( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3)) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 Y0)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 Y0))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))) => 237.26/34.96 (( 237.26/34.96 Y2 = Y1) | 237.26/34.96 (Y2 = Y0)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 Y1) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 setunion( 237.26/34.96 Y0)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y1, 237.26/34.96 Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)), 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)) = 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))))) => 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y3 = Y2)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.96 inference('lazy_cnf_imply', [status(thm)], ['215'])). 237.26/34.96 tff('217', plain, 237.26/34.96 ~ ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 237.26/34.96 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.96 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.96 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.96 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??(Y0)) => 237.26/34.96 ((!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) <=> 237.26/34.96 in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.96 (??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (setadjoin(Y0, Y2) = 237.26/34.96 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> 237.26/34.96 Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i > $o]: 237.26/34.96 (!!((^[Y3 : $i > $o]: 237.26/34.96 ((!!((^[Y4 : $i]: 237.26/34.96 ( 237.26/34.96 in(Y4, 237.26/34.96 Y0) => 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y5 : $i]: 237.26/34.96 (in(Y5, 237.26/34.96 Y1) => 237.26/34.96 (( 237.26/34.96 Y4 = Y5) => 237.26/34.96 (Y2(Y4) <=> 237.26/34.96 Y3(Y5))))))))))) => 237.26/34.96 (dsetconstr(Y0, 237.26/34.96 Y2) = 237.26/34.96 dsetconstr(Y1, 237.26/34.96 Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!(subset(emptyset))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(in(Y2, Y0)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(subset(Y0, 237.26/34.96 Y1)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((~(subset(Y0, Y1))) => 237.26/34.96 (Y0 != Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (Y0 != Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, 237.26/34.96 Y1) => 237.26/34.96 (subset(Y1, 237.26/34.96 Y2) => 237.26/34.96 subset(Y0, 237.26/34.96 Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 subset(Y1, 237.26/34.96 setadjoin(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y2) => 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 in(Y0, 237.26/34.96 powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (subset(Y1, Y0) => 237.26/34.96 (Y0 = Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (subset(Y0, emptyset) => 237.26/34.96 (Y0 = emptyset))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y1, 237.26/34.96 Y0) => 237.26/34.96 in(Y1, 237.26/34.96 powerset( 237.26/34.96 Y0))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 powerset( 237.26/34.96 Y0)) => 237.26/34.96 subset(Y1, 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 in(Y0, 237.26/34.96 powerset(Y0))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 subset( 237.26/34.96 powerset( 237.26/34.96 Y0), 237.26/34.96 powerset( 237.26/34.96 Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 in( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 powerset( 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 subset( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => Y3) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) | 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y1, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y2, Y0) => 237.26/34.96 (subset( 237.26/34.96 Y2, Y1) => 237.26/34.96 subset( 237.26/34.96 Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 Y1, Y0)))))))) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 ~(( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y1))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y1, Y0) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (binintersect( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y1, Y2)) = 237.26/34.96 binunion( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 binintersect( 237.26/34.96 Y0, Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 Y1)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 Y3)) => 237.26/34.96 (( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 ( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3)) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 Y0)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 Y0))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))) => 237.26/34.96 (( 237.26/34.96 Y2 = Y1) | 237.26/34.96 (Y2 = Y0)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 Y1) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 setunion( 237.26/34.96 Y0)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y1, 237.26/34.96 Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)), 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)) = 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))))) => 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y3 = Y2)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.96 inference('lazy_cnf_imply', [status(thm)], ['216'])). 237.26/34.96 tff('218', plain, 237.26/34.96 ~ ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: in(Y0, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.96 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.96 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.96 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??(Y0)) => 237.26/34.96 ((!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) <=> 237.26/34.96 in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.96 (??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (setadjoin(Y0, Y2) = 237.26/34.96 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i > $o]: 237.26/34.96 (!!((^[Y3 : $i > $o]: 237.26/34.96 ((!!((^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 Y0) => 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y5 : $i]: 237.26/34.96 (in(Y5, 237.26/34.96 Y1) => 237.26/34.96 (( 237.26/34.96 Y4 = Y5) => 237.26/34.96 (Y2(Y4) <=> 237.26/34.96 Y3(Y5))))))))))) => 237.26/34.96 (dsetconstr(Y0, 237.26/34.96 Y2) = 237.26/34.96 dsetconstr(Y1, 237.26/34.96 Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!(subset(emptyset))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(in(Y2, Y0)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(subset(Y0, 237.26/34.96 Y1)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((~(subset(Y0, Y1))) => 237.26/34.96 (Y0 != Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (Y0 != Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, 237.26/34.96 Y1) => 237.26/34.96 (subset(Y1, 237.26/34.96 Y2) => 237.26/34.96 subset(Y0, 237.26/34.96 Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 subset(Y1, 237.26/34.96 setadjoin(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, 237.26/34.96 Y2) => 237.26/34.96 subset(Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 in(Y0, 237.26/34.96 powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (subset(Y1, Y0) => 237.26/34.96 (Y0 = Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (subset(Y0, emptyset) => 237.26/34.96 (Y0 = emptyset))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y1, Y0) => 237.26/34.96 in(Y1, 237.26/34.96 powerset(Y0))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 powerset( 237.26/34.96 Y0)) => 237.26/34.96 subset(Y1, 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 in(Y0, powerset(Y0))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 powerset( 237.26/34.96 Y0), 237.26/34.96 powerset( 237.26/34.96 Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 in( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 powerset( 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 subset( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => Y3) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) | 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y1, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y2, Y0) => 237.26/34.96 (subset( 237.26/34.96 Y2, Y1) => 237.26/34.96 subset( 237.26/34.96 Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 Y1, Y0)))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 ~(( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y1))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y1, Y0) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (binintersect( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y1, Y2)) = 237.26/34.96 binunion( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 binintersect( 237.26/34.96 Y0, Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 Y1)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 Y3)) => 237.26/34.96 (( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 ( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3)) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)))) & 237.26/34.96 (setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)) = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 Y0)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 Y0))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))) => 237.26/34.96 (( 237.26/34.96 Y2 = Y1) | 237.26/34.96 (Y2 = Y0)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 powerset( 237.26/34.96 powerset( 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y1) => 237.26/34.96 in( 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)), 237.26/34.96 emptyset)), 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 Y1) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 cartprod( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (??(( 237.26/34.96 ^[Y4 : $i]: 237.26/34.96 (in(Y4, 237.26/34.96 setunion( 237.26/34.96 Y2)) & 237.26/34.96 (Y2 = 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset), 237.26/34.96 setadjoin( 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 setadjoin( 237.26/34.96 Y4, 237.26/34.96 emptyset)), 237.26/34.96 emptyset))))))))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 setunion( 237.26/34.96 Y0)) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y1, 237.26/34.96 Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)), 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (setunion( 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 emptyset)) = 237.26/34.96 Y0)))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))))) => 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y2, 237.26/34.96 emptyset)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 Y1(Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i > $o]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y2) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 Y0) => 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y3 = Y2)))))) => 237.26/34.96 (??(( 237.26/34.96 ^[Y3 : $i]: 237.26/34.96 (in(Y3, 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1)) & 237.26/34.96 (dsetconstr( 237.26/34.96 Y0, Y1) = 237.26/34.96 setadjoin( 237.26/34.96 Y3, 237.26/34.96 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.96 inference('lazy_cnf_imply', [status(thm)], ['217'])). 237.26/34.96 tff('219', plain, 237.26/34.96 ~ ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.96 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.96 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.96 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.96 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.96 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??(Y0)) => 237.26/34.96 ((!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.96 (??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.96 (??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (setadjoin(Y0, Y2) = 237.26/34.96 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 ((??((^[Y1 : $i]: 237.26/34.96 (Y0(Y1) & 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (Y0(Y1) => 237.26/34.96 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i > $o]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 ((Y2 = Y3) => 237.26/34.96 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y0(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y0(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 ((??((^[Y2 : $i]: 237.26/34.96 (Y1(Y2) & 237.26/34.96 (!!((^[Y3 : $i]: 237.26/34.96 (Y1(Y3) => 237.26/34.96 (Y2 = Y3))))))))) => 237.26/34.96 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => 237.26/34.96 (!!((^[Y2 : $i > $o]: 237.26/34.96 (!!((^[Y3 : $i > $o]: 237.26/34.96 ((!!((^[Y4 : $i]: 237.26/34.96 (in(Y4, Y0) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y5 : $i]: 237.26/34.96 (in(Y5, 237.26/34.96 Y1) => 237.26/34.96 (( 237.26/34.96 Y4 = Y5) => 237.26/34.96 (Y2(Y4) <=> 237.26/34.96 Y3(Y5))))))))))) => 237.26/34.96 (dsetconstr(Y0, 237.26/34.96 Y2) = 237.26/34.96 dsetconstr(Y1, 237.26/34.96 Y3)))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1))))) => 237.26/34.96 subset(Y0, Y1)))))))) => 237.26/34.96 ((!!(subset(emptyset))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 in(Y2, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(in(Y2, Y0)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 ((~(subset(Y0, Y1))) => 237.26/34.96 (Y0 != Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (in(Y2, Y0) => 237.26/34.96 ((~(in(Y2, Y1))) => 237.26/34.96 (Y0 != Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (subset(Y1, 237.26/34.96 Y2) => 237.26/34.96 subset(Y0, 237.26/34.96 Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 subset(Y1, 237.26/34.96 setadjoin(Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!((^[Y2 : $i]: 237.26/34.96 (subset(Y0, 237.26/34.96 Y2) => 237.26/34.96 subset(Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, Y2)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 in(Y0, 237.26/34.96 powerset(Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, Y1) => 237.26/34.96 (subset(Y1, Y0) => 237.26/34.96 (Y0 = Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (subset(Y0, emptyset) => 237.26/34.96 (Y0 = emptyset))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y1, Y0) => 237.26/34.96 in(Y1, 237.26/34.96 powerset(Y0))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (in(Y1, 237.26/34.96 powerset(Y0)) => 237.26/34.96 subset(Y1, Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 in(Y0, powerset(Y0))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (subset(Y0, 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 powerset( 237.26/34.96 Y0), 237.26/34.96 powerset( 237.26/34.96 Y1))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 in( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 powerset( 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i > $o]: 237.26/34.96 subset( 237.26/34.96 dsetconstr( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 in(Y1, 237.26/34.96 setadjoin( 237.26/34.96 Y0, 237.26/34.96 setadjoin( 237.26/34.96 Y1, 237.26/34.96 emptyset))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!((^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => Y3) => 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) | 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 Y1, 237.26/34.96 binunion( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y2, Y0) => 237.26/34.96 (subset( 237.26/34.96 Y2, Y1) => 237.26/34.96 subset( 237.26/34.96 Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ((!!((^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0)))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1) => 237.26/34.96 subset( 237.26/34.96 Y1, Y0)))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))) => 237.26/34.96 ((!!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 ~(( 237.26/34.96 ??(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) & 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 (( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 Y1))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y1, Y0) => 237.26/34.96 (binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1) = 237.26/34.96 Y0) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (binintersect( 237.26/34.96 Y0, 237.26/34.96 binunion( 237.26/34.96 Y1, Y2)) = 237.26/34.96 binunion( 237.26/34.96 binintersect( 237.26/34.96 Y0, Y1), 237.26/34.96 binintersect( 237.26/34.96 Y0, Y2)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 in(Y2, 237.26/34.96 Y0))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (subset( 237.26/34.96 Y0, Y1) => 237.26/34.96 (setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (in(Y2, 237.26/34.96 Y0) => 237.26/34.96 in(Y2, 237.26/34.96 Y1)))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))) => 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 Y0)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 Y1) => 237.26/34.96 (~( 237.26/34.96 in(Y2, 237.26/34.96 setminus( 237.26/34.96 Y0, Y1)))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 subset( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1), 237.26/34.96 Y0))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (( 237.26/34.96 setminus( 237.26/34.96 Y0, Y1) = 237.26/34.96 emptyset) => 237.26/34.96 subset( 237.26/34.96 Y0, Y1)))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y1 : $i]: 237.26/34.96 (!!(( 237.26/34.96 ^[Y2 : $i]: 237.26/34.96 (in(Y2, 237.26/34.96 symdiff( 237.26/34.96 Y0, Y1)) => 237.26/34.96 (!!(( 237.26/34.96 ^[Y3 : $o]: 237.26/34.96 (( 237.26/34.96 in(Y2, 237.26/34.96 Y0) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y1))) => 237.26/34.96 Y3)) => 237.26/34.96 (( 237.26/34.96 ( 237.26/34.96 ~( 237.26/34.96 in(Y2, 237.26/34.96 Y0))) => 237.26/34.96 ( 237.26/34.96 in(Y2, 237.26/34.96 Y1) => Y3)) => 237.26/34.96 Y3))))))))))))))) => 237.26/34.96 ( 237.26/34.96 ( 237.26/34.96 !!(( 237.26/34.96 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 Y0)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 Y0))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))) => 237.26/34.97 (( 237.26/34.97 Y2 = Y1) | 237.26/34.97 (Y2 = Y0)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 Y1) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 setunion( 237.26/34.97 Y0)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y1, 237.26/34.97 Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)), 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)) = 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y2 = Y3))))))))))) => 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y3 = Y2)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.97 inference('lazy_cnf_imply', [status(thm)], ['218'])). 237.26/34.97 tff('220', plain, 237.26/34.97 ~ ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 237.26/34.97 (dsetconstr(Y0, Y1) != emptyset)))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.97 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.97 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.97 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.97 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??(Y0)) => 237.26/34.97 ((!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.97 (??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (setadjoin(Y0, Y2) = 237.26/34.97 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => 237.26/34.97 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => 237.26/34.97 (Y2 = Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y2 = Y3))))))))) => 237.26/34.97 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i > $o]: 237.26/34.97 (!!((^[Y3 : $i > $o]: 237.26/34.97 ((!!((^[Y4 : $i]: 237.26/34.97 (in(Y4, Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y5 : $i]: 237.26/34.97 (in(Y5, 237.26/34.97 Y1) => 237.26/34.97 (( 237.26/34.97 Y4 = Y5) => 237.26/34.97 (Y2(Y4) <=> 237.26/34.97 Y3(Y5))))))))))) => 237.26/34.97 (dsetconstr(Y0, Y2) = 237.26/34.97 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!(subset(emptyset))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 in(Y2, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(in(Y2, Y0)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((~(subset(Y0, Y1))) => 237.26/34.97 (Y0 != Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (Y0 != Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y2) => 237.26/34.97 subset(Y0, Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset(Y1, 237.26/34.97 setadjoin(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, 237.26/34.97 Y2) => 237.26/34.97 subset(Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 in(Y0, 237.26/34.97 powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 (Y0 = Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (subset(Y0, emptyset) => 237.26/34.97 (Y0 = emptyset))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 in(Y1, 237.26/34.97 powerset(Y0))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 powerset(Y0)) => 237.26/34.97 subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 in(Y0, powerset(Y0))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 powerset( 237.26/34.97 Y0), 237.26/34.97 powerset( 237.26/34.97 Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 in( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 powerset( 237.26/34.97 Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 subset( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => Y3) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) | 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y1, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y2, Y0) => 237.26/34.97 (subset( 237.26/34.97 Y2, Y1) => 237.26/34.97 subset( 237.26/34.97 Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 Y1, Y0)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 ~(( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y1))))))) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y1, Y0) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (binintersect( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y1, Y2)) = 237.26/34.97 binunion( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 binintersect( 237.26/34.97 Y0, Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 Y1)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 Y3)) => 237.26/34.97 (( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 ( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3)) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 Y0)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 Y0))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))) => 237.26/34.97 (( 237.26/34.97 Y2 = Y1) | 237.26/34.97 (Y2 = Y0)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 Y1) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 setunion( 237.26/34.97 Y0)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y1, 237.26/34.97 Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)), 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)) = 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y2 = Y3))))))))))) => 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y3 = Y2)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.97 inference('lazy_cnf_imply', [status(thm)], ['219'])). 237.26/34.97 tff('221', plain, 237.26/34.97 ~ ((!!((^[Y0 : $i > $o]: (!!((^[Y1 : $i]: (in(Y1, emptyset) => Y0(Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.97 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.97 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.97 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.97 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??(Y0)) => 237.26/34.97 ((!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.97 (??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (setadjoin(Y0, Y2) = 237.26/34.97 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => 237.26/34.97 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y2 = Y3))))))))) => 237.26/34.97 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i > $o]: 237.26/34.97 (!!((^[Y3 : $i > $o]: 237.26/34.97 ((!!((^[Y4 : $i]: 237.26/34.97 (in(Y4, Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y5 : $i]: 237.26/34.97 ( 237.26/34.97 in(Y5, 237.26/34.97 Y1) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 Y4 = Y5) => 237.26/34.97 ( 237.26/34.97 Y2(Y4) <=> 237.26/34.97 Y3(Y5))))))))))) => 237.26/34.97 (dsetconstr(Y0, Y2) = 237.26/34.97 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!(subset(emptyset))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 in(Y2, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(in(Y2, Y0)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((~(subset(Y0, Y1))) => 237.26/34.97 (Y0 != Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (Y0 != Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y2) => 237.26/34.97 subset(Y0, Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset(Y1, 237.26/34.97 setadjoin(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y2) => 237.26/34.97 subset(Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 in(Y0, powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 (Y0 = Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (subset(Y0, emptyset) => 237.26/34.97 (Y0 = emptyset))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 in(Y1, 237.26/34.97 powerset(Y0))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 powerset(Y0)) => 237.26/34.97 subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 in(Y0, powerset(Y0))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 subset( 237.26/34.97 powerset(Y0), 237.26/34.97 powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 in( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 powerset(Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 subset( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 ( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => Y3) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) | 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y1, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y2, Y0) => 237.26/34.97 (subset( 237.26/34.97 Y2, Y1) => 237.26/34.97 subset( 237.26/34.97 Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 Y1, Y0)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 ~(( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y1))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y1, Y0) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1)))))))) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (binintersect( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y1, Y2)) = 237.26/34.97 binunion( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 binintersect( 237.26/34.97 Y0, Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 Y1)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 Y3)) => 237.26/34.97 (( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 ( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3)) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 Y0)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 Y0))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))) => 237.26/34.97 (( 237.26/34.97 Y2 = Y1) | 237.26/34.97 (Y2 = Y0)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 Y1) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 setunion( 237.26/34.97 Y0)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y1, 237.26/34.97 Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)), 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)) = 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y2 = Y3))))))))))) => 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y3 = Y2)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.97 inference('lazy_cnf_imply', [status(thm)], ['220'])). 237.26/34.97 tff('222', plain, 237.26/34.97 ~ ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.97 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.97 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.97 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.97 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??(Y0)) => 237.26/34.97 ((!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.97 (??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (setadjoin(Y0, Y2) = 237.26/34.97 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => 237.26/34.97 (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.97 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i > $o]: 237.26/34.97 (!!((^[Y3 : $i > $o]: 237.26/34.97 ((!!((^[Y4 : $i]: 237.26/34.97 (in(Y4, Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y5 : $i]: 237.26/34.97 (in(Y5, 237.26/34.97 Y1) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 Y4 = Y5) => 237.26/34.97 ( 237.26/34.97 Y2(Y4) <=> 237.26/34.97 Y3(Y5))))))))))) => 237.26/34.97 (dsetconstr(Y0, Y2) = 237.26/34.97 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!(subset(emptyset))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 in(Y2, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(in(Y2, Y0)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((~(subset(Y0, Y1))) => 237.26/34.97 (Y0 != Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (Y0 != Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y2) => 237.26/34.97 subset(Y0, Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset(Y1, 237.26/34.97 setadjoin(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y2) => 237.26/34.97 subset(Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 in(Y0, powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 (Y0 = Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (subset(Y0, emptyset) => 237.26/34.97 (Y0 = emptyset))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 in(Y1, 237.26/34.97 powerset(Y0))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 powerset(Y0)) => 237.26/34.97 subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 in(Y0, powerset(Y0))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 subset( 237.26/34.97 powerset(Y0), 237.26/34.97 powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 in( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 powerset(Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 subset( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => Y3) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) | 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y1, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y2, Y0) => 237.26/34.97 (subset( 237.26/34.97 Y2, Y1) => 237.26/34.97 subset( 237.26/34.97 Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 ~(( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y1))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y1, Y0) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (binintersect( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y1, Y2)) = 237.26/34.97 binunion( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 binintersect( 237.26/34.97 Y0, Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 Y1)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 Y3)) => 237.26/34.97 (( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 ( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3)) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 Y0)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 Y0))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))) => 237.26/34.97 (( 237.26/34.97 Y2 = Y1) | 237.26/34.97 (Y2 = Y0)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 powerset( 237.26/34.97 powerset( 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y1) => 237.26/34.97 in( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)), 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 Y1) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 cartprod( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (??(( 237.26/34.97 ^[Y4 : $i]: 237.26/34.97 (in(Y4, 237.26/34.97 setunion( 237.26/34.97 Y2)) & 237.26/34.97 (Y2 = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 setadjoin( 237.26/34.97 Y4, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 setunion( 237.26/34.97 Y0)) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y1, 237.26/34.97 Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)), 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (setunion( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset)) = 237.26/34.97 Y0)))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y2 = Y3))))))))))) => 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 Y1(Y2)))))))))))) => 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i > $o]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y2) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 Y0) => 237.26/34.97 (Y1(Y3) => 237.26/34.97 (Y3 = Y2)))))) => 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1)) & 237.26/34.97 (dsetconstr( 237.26/34.97 Y0, Y1) = 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.97 inference('lazy_cnf_imply', [status(thm)], ['221'])). 237.26/34.97 tff('223', plain, 237.26/34.97 ~ ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2))))))) => 237.26/34.97 (~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.97 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.97 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.97 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??(Y0)) => 237.26/34.97 ((!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.97 (??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.97 (??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (setadjoin(Y0, Y2) = 237.26/34.97 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 ((??((^[Y1 : $i]: 237.26/34.97 (Y0(Y1) & 237.26/34.97 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i > $o]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 ((Y2 = Y3) => 237.26/34.97 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y0(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.97 ((??((^[Y2 : $i]: 237.26/34.97 (Y1(Y2) & 237.26/34.97 (!!((^[Y3 : $i]: 237.26/34.97 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.97 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => 237.26/34.97 (!!((^[Y2 : $i > $o]: 237.26/34.97 (!!((^[Y3 : $i > $o]: 237.26/34.97 ((!!((^[Y4 : $i]: 237.26/34.97 (in(Y4, Y0) => 237.26/34.97 (!!((^[Y5 : $i]: 237.26/34.97 (in(Y5, 237.26/34.97 Y1) => 237.26/34.97 (( 237.26/34.97 Y4 = Y5) => 237.26/34.97 (Y2(Y4) <=> 237.26/34.97 Y3(Y5))))))))))) => 237.26/34.97 (dsetconstr(Y0, Y2) = 237.26/34.97 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.97 subset(Y0, Y1)))))))) => 237.26/34.97 ((!!(subset(emptyset))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 in(Y2, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(in(Y2, Y0)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 ((~(subset(Y0, Y1))) => 237.26/34.97 (Y0 != Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, Y0) => 237.26/34.97 ((~(in(Y2, Y1))) => 237.26/34.97 (Y0 != Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y2) => 237.26/34.97 subset(Y0, Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset(Y1, 237.26/34.97 setadjoin(Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (subset(Y0, Y2) => 237.26/34.97 subset(Y0, 237.26/34.97 setadjoin(Y1, 237.26/34.97 Y2)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 in(Y0, powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 (Y0 = Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (subset(Y0, emptyset) => 237.26/34.97 (Y0 = emptyset))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y1, Y0) => 237.26/34.97 in(Y1, 237.26/34.97 powerset(Y0))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (in(Y1, 237.26/34.97 powerset(Y0)) => 237.26/34.97 subset(Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 in(Y0, powerset(Y0))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (subset(Y0, Y1) => 237.26/34.97 subset( 237.26/34.97 powerset(Y0), 237.26/34.97 powerset(Y1))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 in( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 powerset(Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i > $o]: 237.26/34.97 subset( 237.26/34.97 dsetconstr( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!((^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 ( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => Y3) => 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) | 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 Y1, 237.26/34.97 binunion( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!((^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y2, Y0) => 237.26/34.97 (subset( 237.26/34.97 Y2, Y1) => 237.26/34.97 subset( 237.26/34.97 Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1) => 237.26/34.97 subset( 237.26/34.97 Y1, Y0)))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))) => 237.26/34.97 ((!!((^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 ~(( 237.26/34.97 ??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) & 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 Y1))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y1, Y0) => 237.26/34.97 (binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y1)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1) = 237.26/34.97 Y0) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ((!!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (binintersect( 237.26/34.97 Y0, 237.26/34.97 binunion( 237.26/34.97 Y1, Y2)) = 237.26/34.97 binunion( 237.26/34.97 binintersect( 237.26/34.97 Y0, Y1), 237.26/34.97 binintersect( 237.26/34.97 Y0, Y2)))))))))))) => 237.26/34.97 (( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 in(Y2, 237.26/34.97 Y0))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (subset( 237.26/34.97 Y0, Y1) => 237.26/34.97 (setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 in(Y2, 237.26/34.97 Y1)))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 Y0)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 setminus( 237.26/34.97 Y0, Y1)))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 subset( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1), 237.26/34.97 Y0))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (( 237.26/34.97 setminus( 237.26/34.97 Y0, Y1) = 237.26/34.97 emptyset) => 237.26/34.97 subset( 237.26/34.97 Y0, Y1)))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1)) => 237.26/34.97 (!!(( 237.26/34.97 ^[Y3 : $o]: 237.26/34.97 (( 237.26/34.97 in(Y2, 237.26/34.97 Y0) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 Y3)) => 237.26/34.97 (( 237.26/34.97 ( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 ( 237.26/34.97 in(Y2, 237.26/34.97 Y1) => Y3)) => 237.26/34.97 Y3))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 Y0) => 237.26/34.97 (in(Y2, 237.26/34.97 Y1) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y0))) => 237.26/34.97 (( 237.26/34.97 ~( 237.26/34.97 in(Y2, 237.26/34.97 Y1))) => 237.26/34.97 (~( 237.26/34.97 in(Y2, 237.26/34.97 symdiff( 237.26/34.97 Y0, Y1))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y0, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 in(Y1, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)) = 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y2, 237.26/34.97 setadjoin( 237.26/34.97 Y3, 237.26/34.97 emptyset)), 237.26/34.97 emptyset))))))))))))))))) => 237.26/34.97 ( 237.26/34.97 ( 237.26/34.97 !!(( 237.26/34.97 ^[Y0 : $i]: 237.26/34.97 (!!(( 237.26/34.97 ^[Y1 : $i]: 237.26/34.97 (??(( 237.26/34.97 ^[Y2 : $i]: 237.26/34.97 (in(Y2, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (??(( 237.26/34.97 ^[Y3 : $i]: 237.26/34.97 (in(Y3, 237.26/34.97 setunion( 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.97 Y1, 237.26/34.97 emptyset)), 237.26/34.97 emptyset)))) & 237.26/34.97 (setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 emptyset), 237.26/34.97 setadjoin( 237.26/34.97 setadjoin( 237.26/34.97 Y0, 237.26/34.97 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 Y0)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 Y0))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))) => 237.26/34.98 (( 237.26/34.98 Y2 = Y1) | 237.26/34.98 (Y2 = Y0)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 Y1) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 setunion( 237.26/34.98 Y0)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y1, 237.26/34.98 Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)), 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)) = 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y2 = Y3))))))))))) => 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y3 = Y2)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.98 inference('lazy_cnf_imply', [status(thm)], ['222'])). 237.26/34.98 tff('224', plain, 237.26/34.98 ~ ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.98 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.98 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.98 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.98 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.98 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??(Y0)) => 237.26/34.98 ((!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.98 (??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (setadjoin(Y0, Y2) = 237.26/34.98 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i > $o]: 237.26/34.98 (!!((^[Y3 : $i > $o]: 237.26/34.98 ((!!((^[Y4 : $i]: 237.26/34.98 (in(Y4, Y0) => 237.26/34.98 (!!((^[Y5 : $i]: 237.26/34.98 (in(Y5, 237.26/34.98 Y1) => 237.26/34.98 (( 237.26/34.98 Y4 = Y5) => 237.26/34.98 (Y2(Y4) <=> 237.26/34.98 Y3(Y5))))))))))) => 237.26/34.98 (dsetconstr(Y0, Y2) = 237.26/34.98 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!(subset(emptyset))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(in(Y2, Y0)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((~(subset(Y0, Y1))) => 237.26/34.98 (Y0 != Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (Y0 != Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y2) => 237.26/34.98 subset(Y0, Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y1, 237.26/34.98 setadjoin(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y2) => 237.26/34.98 subset(Y0, 237.26/34.98 setadjoin(Y1, 237.26/34.98 Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 in(Y0, powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 (Y0 = Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (subset(Y0, emptyset) => 237.26/34.98 (Y0 = emptyset))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 in(Y1, powerset(Y0))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 powerset(Y0)) => 237.26/34.98 subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 in(Y0, powerset(Y0))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 subset( 237.26/34.98 powerset(Y0), 237.26/34.98 powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 in( 237.26/34.98 dsetconstr(Y0, 237.26/34.98 Y1), 237.26/34.98 powerset(Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 subset( 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1), Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => Y3) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) | 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 Y0, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 Y1, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y2, Y0) => 237.26/34.98 (subset( 237.26/34.98 Y2, Y1) => 237.26/34.98 subset( 237.26/34.98 Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 ~(( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y1))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y1, Y0) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1)))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (binintersect( 237.26/34.98 Y0, 237.26/34.98 binunion( 237.26/34.98 Y1, Y2)) = 237.26/34.98 binunion( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 binintersect( 237.26/34.98 Y0, Y2)))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 (setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in(Y2, 237.26/34.98 Y1)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 Y3)) => 237.26/34.98 (( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3)) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 Y0)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 Y0))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))) => 237.26/34.98 (( 237.26/34.98 Y2 = Y1) | 237.26/34.98 (Y2 = Y0)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 Y1) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 setunion( 237.26/34.98 Y0)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y1, 237.26/34.98 Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)), 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)) = 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y2 = Y3))))))))))) => 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y3 = Y2)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.98 inference('lazy_cnf_imply', [status(thm)], ['223'])). 237.26/34.98 tff('225', plain, 237.26/34.98 ~ ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2))))))) => 237.26/34.98 (~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.98 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.98 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.98 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??(Y0)) => 237.26/34.98 ((!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.98 (??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (setadjoin(Y0, Y2) = 237.26/34.98 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i > $o]: 237.26/34.98 (!!((^[Y3 : $i > $o]: 237.26/34.98 ((!!((^[Y4 : $i]: 237.26/34.98 (in(Y4, Y0) => 237.26/34.98 (!!((^[Y5 : $i]: 237.26/34.98 ( 237.26/34.98 in(Y5, 237.26/34.98 Y1) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 Y4 = Y5) => 237.26/34.98 ( 237.26/34.98 Y2(Y4) <=> 237.26/34.98 Y3(Y5))))))))))) => 237.26/34.98 (dsetconstr(Y0, Y2) = 237.26/34.98 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!(subset(emptyset))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(in(Y2, Y0)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((~(subset(Y0, Y1))) => 237.26/34.98 (Y0 != Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (Y0 != Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y2) => 237.26/34.98 subset(Y0, Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y1, 237.26/34.98 setadjoin(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y2) => 237.26/34.98 subset(Y0, 237.26/34.98 setadjoin(Y1, 237.26/34.98 Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 in(Y0, powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 (Y0 = Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (subset(Y0, emptyset) => 237.26/34.98 (Y0 = emptyset))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 in(Y1, powerset(Y0))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (in(Y1, powerset(Y0)) => 237.26/34.98 subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 in(Y0, powerset(Y0))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 subset( 237.26/34.98 powerset(Y0), 237.26/34.98 powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 in( 237.26/34.98 dsetconstr(Y0, 237.26/34.98 Y1), 237.26/34.98 powerset(Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 subset( 237.26/34.98 dsetconstr(Y0, 237.26/34.98 Y1), Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => Y3) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y1) | 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y0, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 Y1, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y2, Y0) => 237.26/34.98 (subset( 237.26/34.98 Y2, Y1) => 237.26/34.98 subset( 237.26/34.98 Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 ( 237.26/34.98 subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 ( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 ~(( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y1))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y1, Y0) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1)))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (binintersect( 237.26/34.98 Y0, 237.26/34.98 binunion( 237.26/34.98 Y1, Y2)) = 237.26/34.98 binunion( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 binintersect( 237.26/34.98 Y0, Y2)))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 (setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in(Y2, 237.26/34.98 Y1)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 Y3)) => 237.26/34.98 (( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3)) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 Y0)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 Y0))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))) => 237.26/34.98 (( 237.26/34.98 Y2 = Y1) | 237.26/34.98 (Y2 = Y0)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 Y1) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 setunion( 237.26/34.98 Y0)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y1, 237.26/34.98 Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)), 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)) = 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y2 = Y3))))))))))) => 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y3 = Y2)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.98 inference('lazy_cnf_imply', [status(thm)], ['224'])). 237.26/34.98 tff('226', plain, 237.26/34.98 ~ ((!!((^[Y0 : $o]: (Y0 => in(emptyset, prop2set(Y0)))))) => 237.26/34.98 ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.98 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.98 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??(Y0)) => 237.26/34.98 ((!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.98 (??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (setadjoin(Y0, Y2) = 237.26/34.98 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i > $o]: 237.26/34.98 (!!((^[Y3 : $i > $o]: 237.26/34.98 ((!!((^[Y4 : $i]: 237.26/34.98 (in(Y4, Y0) => 237.26/34.98 (!!((^[Y5 : $i]: 237.26/34.98 (in(Y5, 237.26/34.98 Y1) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 Y4 = Y5) => 237.26/34.98 ( 237.26/34.98 Y2(Y4) <=> 237.26/34.98 Y3(Y5))))))))))) => 237.26/34.98 (dsetconstr(Y0, Y2) = 237.26/34.98 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!(subset(emptyset))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(in(Y2, Y0)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((~(subset(Y0, Y1))) => 237.26/34.98 (Y0 != Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (Y0 != Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y2) => 237.26/34.98 subset(Y0, Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y1, 237.26/34.98 setadjoin(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y2) => 237.26/34.98 subset(Y0, 237.26/34.98 setadjoin(Y1, Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 in(Y0, powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 (Y0 = Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (subset(Y0, emptyset) => 237.26/34.98 (Y0 = emptyset))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 in(Y1, powerset(Y0))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (in(Y1, powerset(Y0)) => 237.26/34.98 subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 in(Y0, powerset(Y0))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 subset( 237.26/34.98 powerset(Y0), 237.26/34.98 powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 in( 237.26/34.98 dsetconstr(Y0, 237.26/34.98 Y1), 237.26/34.98 powerset(Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 subset( 237.26/34.98 dsetconstr(Y0, 237.26/34.98 Y1), Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin(Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => Y3) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y1) | 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y0, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y1, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y2, Y0) => 237.26/34.98 (subset( 237.26/34.98 Y2, Y1) => 237.26/34.98 subset( 237.26/34.98 Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 ( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 ~(( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y1))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y1, Y0) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (binintersect( 237.26/34.98 Y0, 237.26/34.98 binunion( 237.26/34.98 Y1, Y2)) = 237.26/34.98 binunion( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 binintersect( 237.26/34.98 Y0, Y2)))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))))) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 (setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in(Y2, 237.26/34.98 Y1)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 Y3)) => 237.26/34.98 (( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3)) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 Y0)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 Y0))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))) => 237.26/34.98 (( 237.26/34.98 Y2 = Y1) | 237.26/34.98 (Y2 = Y0)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 Y1) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 setunion( 237.26/34.98 Y0)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y1, 237.26/34.98 Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)), 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)) = 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y2 = Y3))))))))))) => 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y3 = Y2)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.98 inference('lazy_cnf_imply', [status(thm)], ['225'])). 237.26/34.98 tff('227', plain, 237.26/34.98 ~ ((!!((^[Y0 : $o]: (Y0 => set2prop(prop2set(Y0)))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.98 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.98 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??(Y0)) => 237.26/34.98 ((!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.98 (??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.98 (??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (setadjoin(Y0, Y2) = 237.26/34.98 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 ((??((^[Y1 : $i]: 237.26/34.98 (Y0(Y1) & 237.26/34.98 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i > $o]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 ((Y2 = Y3) => 237.26/34.98 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y0(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 ((??((^[Y2 : $i]: 237.26/34.98 (Y1(Y2) & 237.26/34.98 (!!((^[Y3 : $i]: 237.26/34.98 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.98 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((Y0 = Y1) => 237.26/34.98 (!!((^[Y2 : $i > $o]: 237.26/34.98 (!!((^[Y3 : $i > $o]: 237.26/34.98 ((!!((^[Y4 : $i]: 237.26/34.98 (in(Y4, Y0) => 237.26/34.98 (!!((^[Y5 : $i]: 237.26/34.98 (in(Y5, Y1) => 237.26/34.98 (( 237.26/34.98 Y4 = Y5) => 237.26/34.98 ( 237.26/34.98 Y2(Y4) <=> 237.26/34.98 Y3(Y5))))))))))) => 237.26/34.98 (dsetconstr(Y0, Y2) = 237.26/34.98 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.98 subset(Y0, Y1)))))))) => 237.26/34.98 ((!!(subset(emptyset))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(in(Y2, Y0)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ((~(subset(Y0, Y1))) => 237.26/34.98 (Y0 != Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 ((~(in(Y2, Y1))) => 237.26/34.98 (Y0 != Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y2) => 237.26/34.98 subset(Y0, Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (subset(Y0, Y2) => 237.26/34.98 subset(Y0, 237.26/34.98 setadjoin(Y1, Y2)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 in(Y0, powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 (Y0 = Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (subset(Y0, emptyset) => 237.26/34.98 (Y0 = emptyset))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y1, Y0) => 237.26/34.98 in(Y1, powerset(Y0))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (in(Y1, powerset(Y0)) => 237.26/34.98 subset(Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 in(Y0, powerset(Y0))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset(Y0, Y1) => 237.26/34.98 subset( 237.26/34.98 powerset(Y0), 237.26/34.98 powerset(Y1))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 in( 237.26/34.98 dsetconstr(Y0, Y1), 237.26/34.98 powerset(Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i > $o]: 237.26/34.98 subset( 237.26/34.98 dsetconstr(Y0, 237.26/34.98 Y1), Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, Y0) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin(Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => Y3) => 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!((^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) | 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y0, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset(Y1, 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y2, Y0) => 237.26/34.98 (subset( 237.26/34.98 Y2, Y1) => 237.26/34.98 subset( 237.26/34.98 Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!((^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 Y1, Y0)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 ~(( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 Y1))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y1, Y0) => 237.26/34.98 (binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1) = 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ((!!((^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (binintersect( 237.26/34.98 Y0, 237.26/34.98 binunion( 237.26/34.98 Y1, Y2)) = 237.26/34.98 binunion( 237.26/34.98 binintersect( 237.26/34.98 Y0, Y1), 237.26/34.98 binintersect( 237.26/34.98 Y0, Y2)))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 in(Y2, 237.26/34.98 Y0))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))))))))))))) => 237.26/34.98 ((!!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (subset( 237.26/34.98 Y0, Y1) => 237.26/34.98 (setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset)))))))) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in(Y2, 237.26/34.98 Y1)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 Y0)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 setminus( 237.26/34.98 Y0, Y1)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 subset( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1), 237.26/34.98 Y0))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (( 237.26/34.98 setminus( 237.26/34.98 Y0, Y1) = 237.26/34.98 emptyset) => 237.26/34.98 subset( 237.26/34.98 Y0, Y1)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $o]: 237.26/34.98 (( 237.26/34.98 in(Y2, 237.26/34.98 Y0) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 Y3)) => 237.26/34.98 (( 237.26/34.98 ( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 ( 237.26/34.98 in(Y2, 237.26/34.98 Y1) => Y3)) => 237.26/34.98 Y3))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (in(Y2, 237.26/34.98 Y1) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y0))) => 237.26/34.98 (( 237.26/34.98 ~( 237.26/34.98 in(Y2, 237.26/34.98 Y1))) => 237.26/34.98 (~( 237.26/34.98 in(Y2, 237.26/34.98 symdiff( 237.26/34.98 Y0, Y1))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 in(Y1, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)))) & 237.26/34.98 (setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)) = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 Y0)))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 Y0))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 setadjoin( 237.26/34.98 Y1, 237.26/34.98 emptyset))) => 237.26/34.98 (( 237.26/34.98 Y2 = Y1) | 237.26/34.98 (Y2 = Y0)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 subset( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 powerset( 237.26/34.98 powerset( 237.26/34.98 binunion( 237.26/34.98 Y0, Y1)))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y1) => 237.26/34.98 in( 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset)), 237.26/34.98 emptyset)), 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 Y1) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 cartprod( 237.26/34.98 Y0, Y1)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (??(( 237.26/34.98 ^[Y4 : $i]: 237.26/34.98 (in(Y4, 237.26/34.98 setunion( 237.26/34.98 Y2)) & 237.26/34.98 (Y2 = 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 emptyset), 237.26/34.98 setadjoin( 237.26/34.98 setadjoin( 237.26/34.98 Y3, 237.26/34.98 setadjoin( 237.26/34.98 Y4, 237.26/34.98 emptyset)), 237.26/34.98 emptyset))))))))))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i]: 237.26/34.98 (in(Y1, 237.26/34.98 setunion( 237.26/34.98 Y0)) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 in(Y1, 237.26/34.98 Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)), 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 subset( 237.26/34.98 Y0, 237.26/34.98 setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (setunion( 237.26/34.98 setadjoin( 237.26/34.98 Y0, 237.26/34.98 emptyset)) = 237.26/34.98 Y0)))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (!!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (Y1(Y3) => 237.26/34.98 (Y2 = Y3))))))))))) => 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))))))))))) => 237.26/34.98 ( 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (( 237.26/34.98 ??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 dsetconstr( 237.26/34.98 Y0, Y1)) & 237.26/34.98 (dsetconstr( 237.26/34.98 Y0, Y1) = 237.26/34.98 setadjoin( 237.26/34.98 Y2, 237.26/34.98 emptyset)))))) => 237.26/34.98 (??(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) & 237.26/34.98 Y1(Y2)))))))))))) => 237.26/34.98 ( 237.26/34.98 !!(( 237.26/34.98 ^[Y0 : $i]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y1 : $i > $o]: 237.26/34.98 (!!(( 237.26/34.98 ^[Y2 : $i]: 237.26/34.98 (in(Y2, 237.26/34.98 Y0) => 237.26/34.98 (Y1(Y2) => 237.26/34.98 (( 237.26/34.98 !!(( 237.26/34.98 ^[Y3 : $i]: 237.26/34.98 (in(Y3, 237.26/34.98 Y0) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y3 = Y2)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.99 inference('lazy_cnf_imply', [status(thm)], ['226'])). 237.26/34.99 tff('228', plain, 237.26/34.99 ~ ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))))) => 237.26/34.99 (!!((^[Y2 : $i]: (in(Y2, Y0) => (~(Y1(Y2)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.99 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??(Y0)) => 237.26/34.99 ((!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.99 (??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.99 (??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (setadjoin(Y0, Y2) = 237.26/34.99 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i > $o]: 237.26/34.99 (!!((^[Y3 : $i > $o]: 237.26/34.99 ((!!((^[Y4 : $i]: 237.26/34.99 (in(Y4, Y0) => 237.26/34.99 (!!((^[Y5 : $i]: 237.26/34.99 (in(Y5, Y1) => 237.26/34.99 ((Y4 = Y5) => 237.26/34.99 (Y2(Y4) <=> 237.26/34.99 Y3(Y5))))))))))) => 237.26/34.99 (dsetconstr(Y0, Y2) = 237.26/34.99 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!(subset(emptyset))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(in(Y2, Y0)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (Y0 != Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y2) => 237.26/34.99 subset(Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y2) => 237.26/34.99 subset(Y0, 237.26/34.99 setadjoin(Y1, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 in(Y0, powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y0) => 237.26/34.99 (Y0 = Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (subset(Y0, emptyset) => 237.26/34.99 (Y0 = emptyset))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y1, Y0) => 237.26/34.99 in(Y1, powerset(Y0))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (in(Y1, powerset(Y0)) => 237.26/34.99 subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 subset(powerset(Y0), 237.26/34.99 powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 in( 237.26/34.99 dsetconstr(Y0, Y1), 237.26/34.99 powerset(Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 subset( 237.26/34.99 dsetconstr(Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin(Y0, 237.26/34.99 setadjoin(Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => Y3) => 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) | 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y0, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y2, Y0) => 237.26/34.99 (subset( 237.26/34.99 Y2, Y1) => 237.26/34.99 subset( 237.26/34.99 Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 ~(( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))) => 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y1))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y1, Y0) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (binintersect( 237.26/34.99 Y0, 237.26/34.99 binunion( 237.26/34.99 Y1, Y2)) = 237.26/34.99 binunion( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 binintersect( 237.26/34.99 Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 (setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in(Y2, 237.26/34.99 Y1)))))))))))) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 Y3)) => 237.26/34.99 (( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3)) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 Y0)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 Y0))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))) => 237.26/34.99 (( 237.26/34.99 Y2 = Y1) | 237.26/34.99 (Y2 = Y0)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 Y1) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 setunion( 237.26/34.99 Y0)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y1, 237.26/34.99 Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)), 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)) = 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y2 = Y3))))))))))) => 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y3 = Y2)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.99 inference('lazy_cnf_imply', [status(thm)], ['227'])). 237.26/34.99 tff('229', plain, 237.26/34.99 ~ ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((~((!!((^[Y2 : $i]: (in(Y2, Y0) => Y1(Y2))))))) => 237.26/34.99 (??((^[Y2 : $i]: (in(Y2, Y0) & (~(Y1(Y2)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??(Y0)) => 237.26/34.99 ((!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.99 (??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.99 (??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (setadjoin(Y0, Y2) = 237.26/34.99 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i > $o]: 237.26/34.99 (!!((^[Y3 : $i > $o]: 237.26/34.99 ((!!((^[Y4 : $i]: 237.26/34.99 (in(Y4, Y0) => 237.26/34.99 (!!((^[Y5 : $i]: 237.26/34.99 (in(Y5, Y1) => 237.26/34.99 ((Y4 = Y5) => 237.26/34.99 (Y2(Y4) <=> 237.26/34.99 Y3(Y5))))))))))) => 237.26/34.99 (dsetconstr(Y0, Y2) = 237.26/34.99 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!(subset(emptyset))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(in(Y2, Y0)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (Y0 != Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y2) => 237.26/34.99 subset(Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y2) => 237.26/34.99 subset(Y0, 237.26/34.99 setadjoin(Y1, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 in(Y0, powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y0) => 237.26/34.99 (Y0 = Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (subset(Y0, emptyset) => 237.26/34.99 (Y0 = emptyset))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y1, Y0) => 237.26/34.99 in(Y1, powerset(Y0))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (in(Y1, powerset(Y0)) => 237.26/34.99 subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 subset(powerset(Y0), 237.26/34.99 powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 in( 237.26/34.99 dsetconstr(Y0, Y1), 237.26/34.99 powerset(Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 subset( 237.26/34.99 dsetconstr(Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin(Y0, 237.26/34.99 setadjoin(Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => Y3) => 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) | 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y0, 237.26/34.99 binunion(Y0, 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 ( 237.26/34.99 subset( 237.26/34.99 Y2, Y0) => 237.26/34.99 ( 237.26/34.99 subset( 237.26/34.99 Y2, Y1) => 237.26/34.99 subset( 237.26/34.99 Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 ~(( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))) => 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y1))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y1, Y0) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (binintersect( 237.26/34.99 Y0, 237.26/34.99 binunion( 237.26/34.99 Y1, Y2)) = 237.26/34.99 binunion( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 binintersect( 237.26/34.99 Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 (setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in(Y2, 237.26/34.99 Y1)))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))))) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 Y3)) => 237.26/34.99 (( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3)) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 Y0)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 Y0))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))) => 237.26/34.99 (( 237.26/34.99 Y2 = Y1) | 237.26/34.99 (Y2 = Y0)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 Y1) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 setunion( 237.26/34.99 Y0)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y1, 237.26/34.99 Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)), 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)) = 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y2 = Y3))))))))))) => 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y3 = Y2)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.99 inference('lazy_cnf_imply', [status(thm)], ['228'])). 237.26/34.99 tff('230', plain, 237.26/34.99 ~ ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??(Y0)) => 237.26/34.99 ((!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.99 (??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.99 (??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (setadjoin(Y0, Y2) = 237.26/34.99 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i > $o]: 237.26/34.99 (!!((^[Y3 : $i > $o]: 237.26/34.99 ((!!((^[Y4 : $i]: 237.26/34.99 (in(Y4, Y0) => 237.26/34.99 (!!((^[Y5 : $i]: 237.26/34.99 (in(Y5, Y1) => 237.26/34.99 ((Y4 = Y5) => 237.26/34.99 (Y2(Y4) <=> 237.26/34.99 Y3(Y5))))))))))) => 237.26/34.99 (dsetconstr(Y0, Y2) = 237.26/34.99 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!(subset(emptyset))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(in(Y2, Y0)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (Y0 != Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y2) => 237.26/34.99 subset(Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y2) => 237.26/34.99 subset(Y0, 237.26/34.99 setadjoin(Y1, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 in(Y0, powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (subset(Y0, emptyset) => 237.26/34.99 (Y0 = emptyset))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y1, Y0) => 237.26/34.99 in(Y1, powerset(Y0))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (in(Y1, powerset(Y0)) => 237.26/34.99 subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 subset(powerset(Y0), 237.26/34.99 powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 in(dsetconstr(Y0, Y1), 237.26/34.99 powerset(Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 subset( 237.26/34.99 dsetconstr(Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin(Y0, 237.26/34.99 setadjoin(Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => Y3) => 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) | 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y0, 237.26/34.99 binunion(Y0, 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, 237.26/34.99 binunion(Y0, 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y2, Y0) => 237.26/34.99 ( 237.26/34.99 subset( 237.26/34.99 Y2, Y1) => 237.26/34.99 subset( 237.26/34.99 Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 ~(( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y1))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 subset( 237.26/34.99 Y1, Y0) => 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (binintersect( 237.26/34.99 Y0, 237.26/34.99 binunion( 237.26/34.99 Y1, Y2)) = 237.26/34.99 binunion( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 binintersect( 237.26/34.99 Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 (setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in(Y2, 237.26/34.99 Y1)))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 Y3)) => 237.26/34.99 (( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3)) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 Y0)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 Y0))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))) => 237.26/34.99 (( 237.26/34.99 Y2 = Y1) | 237.26/34.99 (Y2 = Y0)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 Y1) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 setunion( 237.26/34.99 Y0)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y1, 237.26/34.99 Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)), 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)) = 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y2 = Y3))))))))))) => 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y3 = Y2)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.99 inference('lazy_cnf_imply', [status(thm)], ['229'])). 237.26/34.99 tff('231', plain, 237.26/34.99 ~ ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: (!!((^[Y2 : $i]: (Y0(Y2) <=> (Y2 = Y1)))))))) => 237.26/34.99 (??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.99 (??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (setadjoin(Y0, Y2) = 237.26/34.99 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i > $o]: 237.26/34.99 (!!((^[Y3 : $i > $o]: 237.26/34.99 ((!!((^[Y4 : $i]: 237.26/34.99 (in(Y4, Y0) => 237.26/34.99 (!!((^[Y5 : $i]: 237.26/34.99 (in(Y5, Y1) => 237.26/34.99 ((Y4 = Y5) => 237.26/34.99 (Y2(Y4) <=> 237.26/34.99 Y3(Y5))))))))))) => 237.26/34.99 (dsetconstr(Y0, Y2) = 237.26/34.99 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!(subset(emptyset))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(in(Y2, Y0)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (Y0 != Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y2) => 237.26/34.99 subset(Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y2) => 237.26/34.99 subset(Y0, 237.26/34.99 setadjoin(Y1, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 in(Y0, powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (subset(Y0, emptyset) => 237.26/34.99 (Y0 = emptyset))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y1, Y0) => 237.26/34.99 in(Y1, powerset(Y0))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (in(Y1, powerset(Y0)) => 237.26/34.99 subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 subset(powerset(Y0), 237.26/34.99 powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 in(dsetconstr(Y0, Y1), 237.26/34.99 powerset(Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 subset( 237.26/34.99 dsetconstr(Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin(Y0, 237.26/34.99 setadjoin(Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => Y3) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) | 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y0, 237.26/34.99 binunion(Y0, 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, 237.26/34.99 binunion(Y0, 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y2, Y0) => 237.26/34.99 (subset( 237.26/34.99 Y2, Y1) => 237.26/34.99 subset( 237.26/34.99 Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 ~(( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y1))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y1, Y0) => 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (binintersect( 237.26/34.99 Y0, 237.26/34.99 binunion( 237.26/34.99 Y1, Y2)) = 237.26/34.99 binunion( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 binintersect( 237.26/34.99 Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 (setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in(Y2, 237.26/34.99 Y1)))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 Y3)) => 237.26/34.99 (( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3)) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)))) & 237.26/34.99 (setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)) = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 Y0)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 Y0))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/34.99 emptyset))) => 237.26/34.99 (( 237.26/34.99 Y2 = Y1) | 237.26/34.99 (Y2 = Y0)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 powerset( 237.26/34.99 powerset( 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y1) => 237.26/34.99 in( 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset)), 237.26/34.99 emptyset)), 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 Y1) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 cartprod( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (??(( 237.26/34.99 ^[Y4 : $i]: 237.26/34.99 (in(Y4, 237.26/34.99 setunion( 237.26/34.99 Y2)) & 237.26/34.99 (Y2 = 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset), 237.26/34.99 setadjoin( 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 setadjoin( 237.26/34.99 Y4, 237.26/34.99 emptyset)), 237.26/34.99 emptyset))))))))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (in(Y1, 237.26/34.99 setunion( 237.26/34.99 Y0)) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y1, 237.26/34.99 Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)), 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 subset( 237.26/34.99 Y0, 237.26/34.99 setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (setunion( 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 emptyset)) = 237.26/34.99 Y0)))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y2 = Y3))))))))))) => 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y2, 237.26/34.99 emptyset)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 Y1(Y2)))))))))))) => 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i > $o]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y2) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 Y0) => 237.26/34.99 (Y1(Y3) => 237.26/34.99 (Y3 = Y2)))))) => 237.26/34.99 (??(( 237.26/34.99 ^[Y3 : $i]: 237.26/34.99 (in(Y3, 237.26/34.99 dsetconstr( 237.26/34.99 Y0, Y1)) & 237.26/34.99 (dsetconstr( 237.26/34.99 Y0, Y1) = 237.26/34.99 setadjoin( 237.26/34.99 Y3, 237.26/34.99 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/34.99 inference('lazy_cnf_imply', [status(thm)], ['230'])). 237.26/34.99 tff('232', plain, 237.26/34.99 ~ ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (in(Y2, Y0) => in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/34.99 (??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => 237.26/34.99 (setadjoin(Y0, Y2) = 237.26/34.99 setadjoin(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 ((??((^[Y1 : $i]: 237.26/34.99 (Y0(Y1) & 237.26/34.99 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i > $o]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y0(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 ((??((^[Y2 : $i]: 237.26/34.99 (Y1(Y2) & 237.26/34.99 (!!((^[Y3 : $i]: 237.26/34.99 (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/34.99 (descr(Y0) = descr(Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((Y0 = Y1) => 237.26/34.99 (!!((^[Y2 : $i > $o]: 237.26/34.99 (!!((^[Y3 : $i > $o]: 237.26/34.99 ((!!((^[Y4 : $i]: 237.26/34.99 (in(Y4, Y0) => 237.26/34.99 (!!((^[Y5 : $i]: 237.26/34.99 (in(Y5, Y1) => 237.26/34.99 ((Y4 = Y5) => 237.26/34.99 (Y2(Y4) <=> 237.26/34.99 Y3(Y5))))))))))) => 237.26/34.99 (dsetconstr(Y0, Y2) = 237.26/34.99 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/34.99 subset(Y0, Y1)))))))) => 237.26/34.99 ((!!(subset(emptyset))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(in(Y2, Y0)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (~(subset(Y0, Y1)))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 ((~(in(Y2, Y1))) => 237.26/34.99 (Y0 != Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y2) => 237.26/34.99 subset(Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset(Y0, Y2) => 237.26/34.99 subset(Y0, 237.26/34.99 setadjoin(Y1, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 in(Y0, powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (subset(Y0, emptyset) => 237.26/34.99 (Y0 = emptyset))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y1, Y0) => 237.26/34.99 in(Y1, powerset(Y0))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (in(Y1, powerset(Y0)) => 237.26/34.99 subset(Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, Y1) => 237.26/34.99 subset(powerset(Y0), 237.26/34.99 powerset(Y1))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 in(dsetconstr(Y0, Y1), 237.26/34.99 powerset(Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i > $o]: 237.26/34.99 subset( 237.26/34.99 dsetconstr(Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y0) => 237.26/34.99 in(Y2, 237.26/34.99 binunion(Y0, 237.26/34.99 Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin(Y0, 237.26/34.99 setadjoin(Y1, 237.26/34.99 emptyset))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => Y3) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binunion( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (in(Y2, Y1) | 237.26/34.99 in(Y2, Y0)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y0, 237.26/34.99 binunion(Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset(Y1, 237.26/34.99 binunion(Y0, 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y2, Y0) => 237.26/34.99 (subset( 237.26/34.99 Y2, Y1) => 237.26/34.99 subset( 237.26/34.99 Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!((^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset(Y0, 237.26/34.99 Y1) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ((binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1) => 237.26/34.99 subset( 237.26/34.99 Y1, Y0)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 ~(( 237.26/34.99 ??(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) & 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))) => 237.26/34.99 ( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 Y1))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!((^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y1, Y0) => 237.26/34.99 (binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1) = 237.26/34.99 Y0) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (binintersect( 237.26/34.99 Y0, 237.26/34.99 binunion( 237.26/34.99 Y1, Y2)) = 237.26/34.99 binunion( 237.26/34.99 binintersect( 237.26/34.99 Y0, Y1), 237.26/34.99 binintersect( 237.26/34.99 Y0, Y2)))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 in(Y2, 237.26/34.99 Y0))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))))))))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (subset( 237.26/34.99 Y0, Y1) => 237.26/34.99 (setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset)))))))) => 237.26/34.99 ((!!((^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 in(Y2, 237.26/34.99 Y1)))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 Y0)))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 setminus( 237.26/34.99 Y0, Y1)))))))))))))) => 237.26/34.99 ((!!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 subset( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1), 237.26/34.99 Y0))))))) => 237.26/34.99 (( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (( 237.26/34.99 setminus( 237.26/34.99 Y0, Y1) = 237.26/34.99 emptyset) => 237.26/34.99 subset( 237.26/34.99 Y0, Y1)))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1)) => 237.26/34.99 (!!(( 237.26/34.99 ^[Y3 : $o]: 237.26/34.99 (( 237.26/34.99 in(Y2, 237.26/34.99 Y0) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 Y3)) => 237.26/34.99 (( 237.26/34.99 ( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 ( 237.26/34.99 in(Y2, 237.26/34.99 Y1) => Y3)) => 237.26/34.99 Y3))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (in(Y2, 237.26/34.99 Y0) => 237.26/34.99 (in(Y2, 237.26/34.99 Y1) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y2 : $i]: 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y0))) => 237.26/34.99 (( 237.26/34.99 ~( 237.26/34.99 in(Y2, 237.26/34.99 Y1))) => 237.26/34.99 (~( 237.26/34.99 in(Y2, 237.26/34.99 symdiff( 237.26/34.99 Y0, Y1))))))))))))))) => 237.26/34.99 ( 237.26/34.99 ( 237.26/34.99 !!(( 237.26/34.99 ^[Y0 : $i]: 237.26/34.99 (!!(( 237.26/34.99 ^[Y1 : $i]: 237.26/34.99 in(Y1, 237.26/34.99 setadjoin( 237.26/34.99 Y0, 237.26/34.99 setadjoin( 237.26/34.99 Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 Y0)))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 Y0))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))) => 237.26/35.00 (( 237.26/35.00 Y2 = Y1) | 237.26/35.00 (Y2 = Y0)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 Y1) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 setunion( 237.26/35.00 Y0)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y1, 237.26/35.00 Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)), 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)) = 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y2 = Y3))))))))))) => 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y3 = Y2)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.00 inference('lazy_cnf_imply', [status(thm)], ['231'])). 237.26/35.00 tff('233', plain, 237.26/35.00 ~ ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (in(Y2, Y0) <=> in(Y3, Y1)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 ((??((^[Y1 : $i]: 237.26/35.00 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/35.00 (??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => 237.26/35.00 (setadjoin(Y0, Y2) = 237.26/35.00 setadjoin(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 ((??((^[Y1 : $i]: 237.26/35.00 (Y0(Y1) & 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i > $o]: 237.26/35.00 (!!((^[Y3 : $i > $o]: 237.26/35.00 ((!!((^[Y4 : $i]: 237.26/35.00 (in(Y4, Y0) => 237.26/35.00 (!!((^[Y5 : $i]: 237.26/35.00 (in(Y5, Y1) => 237.26/35.00 ((Y4 = Y5) => 237.26/35.00 (Y2(Y4) <=> 237.26/35.00 Y3(Y5))))))))))) => 237.26/35.00 (dsetconstr(Y0, Y2) = 237.26/35.00 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!(subset(emptyset))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 ((~(in(Y2, Y1))) => 237.26/35.00 (~(in(Y2, Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => 237.26/35.00 (~(subset(Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y2) => 237.26/35.00 subset(Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y2) => 237.26/35.00 subset(Y0, 237.26/35.00 setadjoin(Y1, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 in(Y0, powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (subset(Y0, emptyset) => 237.26/35.00 (Y0 = emptyset))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y1, Y0) => 237.26/35.00 in(Y1, powerset(Y0))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (in(Y1, powerset(Y0)) => 237.26/35.00 subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 subset(powerset(Y0), 237.26/35.00 powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 in(dsetconstr(Y0, Y1), 237.26/35.00 powerset(Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 subset( 237.26/35.00 dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin(Y0, 237.26/35.00 setadjoin(Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $o]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => Y3) => 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (in(Y2, Y1) | 237.26/35.00 in(Y2, Y0)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y0, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 ( 237.26/35.00 subset( 237.26/35.00 Y2, Y0) => 237.26/35.00 ( 237.26/35.00 subset( 237.26/35.00 Y2, Y1) => 237.26/35.00 subset( 237.26/35.00 Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, 237.26/35.00 Y1) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1) => 237.26/35.00 subset(Y1, 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 ~(( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))) => 237.26/35.00 ( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 Y1))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y1, Y0) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (binintersect( 237.26/35.00 Y0, 237.26/35.00 binunion( 237.26/35.00 Y1, Y2)) = 237.26/35.00 binunion( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 binintersect( 237.26/35.00 Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y0, Y1) => 237.26/35.00 (setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in(Y2, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y0)))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $o]: 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 Y3)) => 237.26/35.00 (( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3)) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 Y0)))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 Y0))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))) => 237.26/35.00 (( 237.26/35.00 Y2 = Y1) | 237.26/35.00 (Y2 = Y0)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 Y1) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 setunion( 237.26/35.00 Y0)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y1, 237.26/35.00 Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)), 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)) = 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y2 = Y3))))))))))) => 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y3 = Y2)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.00 inference('lazy_cnf_imply', [status(thm)], ['232'])). 237.26/35.00 tff('234', plain, 237.26/35.00 ~ ((!!((^[Y0 : $i > $o]: 237.26/35.00 ((??((^[Y1 : $i]: 237.26/35.00 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/35.00 (??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => 237.26/35.00 (setadjoin(Y0, Y2) = setadjoin(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 ((??((^[Y1 : $i]: 237.26/35.00 (Y0(Y1) & 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i > $o]: 237.26/35.00 (!!((^[Y3 : $i > $o]: 237.26/35.00 ((!!((^[Y4 : $i]: 237.26/35.00 (in(Y4, Y0) => 237.26/35.00 (!!((^[Y5 : $i]: 237.26/35.00 (in(Y5, Y1) => 237.26/35.00 ((Y4 = Y5) => 237.26/35.00 (Y2(Y4) <=> 237.26/35.00 Y3(Y5))))))))))) => 237.26/35.00 (dsetconstr(Y0, Y2) = 237.26/35.00 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!(subset(emptyset))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 ((~(in(Y2, Y1))) => 237.26/35.00 (~(in(Y2, Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => 237.26/35.00 (~(subset(Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y2) => 237.26/35.00 subset(Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y2) => 237.26/35.00 subset(Y0, 237.26/35.00 setadjoin(Y1, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 in(Y0, powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (subset(Y0, emptyset) => 237.26/35.00 (Y0 = emptyset))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y1, Y0) => 237.26/35.00 in(Y1, powerset(Y0))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (in(Y1, powerset(Y0)) => 237.26/35.00 subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 subset(powerset(Y0), 237.26/35.00 powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 in(dsetconstr(Y0, Y1), 237.26/35.00 powerset(Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 subset( 237.26/35.00 dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin(Y0, 237.26/35.00 setadjoin(Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $o]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => Y3) => 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (in(Y2, Y1) | 237.26/35.00 in(Y2, Y0)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y0, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y2, Y0) => 237.26/35.00 ( 237.26/35.00 subset( 237.26/35.00 Y2, Y1) => 237.26/35.00 subset( 237.26/35.00 Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, 237.26/35.00 Y1) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1) => 237.26/35.00 subset(Y1, 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 Y1))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 subset( 237.26/35.00 Y1, Y0) => 237.26/35.00 ( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (binintersect( 237.26/35.00 Y0, 237.26/35.00 binunion( 237.26/35.00 Y1, Y2)) = 237.26/35.00 binunion( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 binintersect( 237.26/35.00 Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y0, Y1) => 237.26/35.00 (setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in(Y2, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $o]: 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 Y3)) => 237.26/35.00 (( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3)) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 Y0)))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 Y0))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))) => 237.26/35.00 (( 237.26/35.00 Y2 = Y1) | 237.26/35.00 (Y2 = Y0)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 Y1) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 setunion( 237.26/35.00 Y0)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y1, 237.26/35.00 Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)), 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)) = 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y2 = Y3))))))))))) => 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y3 = Y2)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.00 inference('lazy_cnf_imply', [status(thm)], ['233'])). 237.26/35.00 tff('235', plain, 237.26/35.00 ~ ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) <=> 237.26/35.00 (??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => 237.26/35.00 (setadjoin(Y0, Y2) = setadjoin(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 ((??((^[Y1 : $i]: 237.26/35.00 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i > $o]: 237.26/35.00 (!!((^[Y3 : $i > $o]: 237.26/35.00 ((!!((^[Y4 : $i]: 237.26/35.00 (in(Y4, Y0) => 237.26/35.00 (!!((^[Y5 : $i]: 237.26/35.00 (in(Y5, Y1) => 237.26/35.00 ((Y4 = Y5) => 237.26/35.00 (Y2(Y4) <=> 237.26/35.00 Y3(Y5))))))))))) => 237.26/35.00 (dsetconstr(Y0, Y2) = 237.26/35.00 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!(subset(emptyset))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => 237.26/35.00 (~(subset(Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y2) => 237.26/35.00 subset(Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y2) => 237.26/35.00 subset(Y0, 237.26/35.00 setadjoin(Y1, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 in(Y0, powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y1, Y0) => 237.26/35.00 in(Y1, powerset(Y0))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (in(Y1, powerset(Y0)) => 237.26/35.00 subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 subset(powerset(Y0), 237.26/35.00 powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 in(dsetconstr(Y0, Y1), 237.26/35.00 powerset(Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 subset(dsetconstr(Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin(Y0, 237.26/35.00 setadjoin(Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $o]: 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => Y3) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (in(Y2, Y1) | 237.26/35.00 in(Y2, Y0)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y0, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y2, Y0) => 237.26/35.00 (subset( 237.26/35.00 Y2, Y1) => 237.26/35.00 subset( 237.26/35.00 Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1) => 237.26/35.00 subset(Y1, 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 Y1))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y1, Y0) => 237.26/35.00 ( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (binintersect( 237.26/35.00 Y0, 237.26/35.00 binunion( 237.26/35.00 Y1, Y2)) = 237.26/35.00 binunion( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 binintersect( 237.26/35.00 Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y0, Y1) => 237.26/35.00 (setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in(Y2, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $o]: 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 Y3)) => 237.26/35.00 (( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3)) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 Y0)))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 Y0))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))) => 237.26/35.00 (( 237.26/35.00 Y2 = Y1) | 237.26/35.00 (Y2 = Y0)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 Y1) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 setunion( 237.26/35.00 Y0)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y1, 237.26/35.00 Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)), 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)) = 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y2 = Y3))))))))))) => 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y3 = Y2)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.00 inference('lazy_cnf_imply', [status(thm)], ['234'])). 237.26/35.00 tff('236', plain, 237.26/35.00 ~ ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => 237.26/35.00 (setadjoin(Y0, Y2) = setadjoin(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 ((??((^[Y1 : $i]: 237.26/35.00 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i > $o]: 237.26/35.00 (!!((^[Y3 : $i > $o]: 237.26/35.00 ((!!((^[Y4 : $i]: 237.26/35.00 (in(Y4, Y0) => 237.26/35.00 (!!((^[Y5 : $i]: 237.26/35.00 (in(Y5, Y1) => 237.26/35.00 ((Y4 = Y5) => 237.26/35.00 (Y2(Y4) <=> Y3(Y5))))))))))) => 237.26/35.00 (dsetconstr(Y0, Y2) = 237.26/35.00 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!(subset(emptyset))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => 237.26/35.00 (~(subset(Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y2) => 237.26/35.00 subset(Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y2) => 237.26/35.00 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 in(Y0, powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y1, Y0) => 237.26/35.00 in(Y1, powerset(Y0))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (in(Y1, powerset(Y0)) => 237.26/35.00 subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 subset(powerset(Y0), 237.26/35.00 powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 in(dsetconstr(Y0, Y1), 237.26/35.00 powerset(Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 subset(dsetconstr(Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin(Y0, 237.26/35.00 setadjoin(Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $o]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => Y3) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion(Y0, 237.26/35.00 Y1)) => 237.26/35.00 (in(Y2, Y1) | 237.26/35.00 in(Y2, Y0)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y0, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y2, 237.26/35.00 Y0) => 237.26/35.00 (subset( 237.26/35.00 Y2, Y1) => 237.26/35.00 subset( 237.26/35.00 Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1) => 237.26/35.00 subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 Y1))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y1, Y0) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (binintersect( 237.26/35.00 Y0, 237.26/35.00 binunion( 237.26/35.00 Y1, Y2)) = 237.26/35.00 binunion( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 binintersect( 237.26/35.00 Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 subset( 237.26/35.00 Y0, Y1) => 237.26/35.00 ( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in(Y2, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $o]: 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 Y3)) => 237.26/35.00 (( 237.26/35.00 ( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3)) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (in(Y2, 237.26/35.00 Y1) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y0))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 symdiff( 237.26/35.00 Y0, Y1))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)))) & 237.26/35.00 (setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)) = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 Y0)))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 Y0))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 setadjoin( 237.26/35.00 Y1, 237.26/35.00 emptyset))) => 237.26/35.00 (( 237.26/35.00 Y2 = Y1) | 237.26/35.00 (Y2 = Y0)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 subset( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 powerset( 237.26/35.00 powerset( 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y1) => 237.26/35.00 in( 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)), 237.26/35.00 emptyset)), 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 Y1) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 cartprod( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (??(( 237.26/35.00 ^[Y4 : $i]: 237.26/35.00 (in(Y4, 237.26/35.00 setunion( 237.26/35.00 Y2)) & 237.26/35.00 (Y2 = 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset), 237.26/35.00 setadjoin( 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 setadjoin( 237.26/35.00 Y4, 237.26/35.00 emptyset)), 237.26/35.00 emptyset))))))))))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (in(Y1, 237.26/35.00 setunion( 237.26/35.00 Y0)) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y1, 237.26/35.00 Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)), 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 subset( 237.26/35.00 Y0, 237.26/35.00 setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (setunion( 237.26/35.00 setadjoin( 237.26/35.00 Y0, 237.26/35.00 emptyset)) = 237.26/35.00 Y0)))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (!!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y2 = Y3))))))))))) => 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))))))))))) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (( 237.26/35.00 ??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y2, 237.26/35.00 emptyset)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 Y1(Y2)))))))))))) => 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i > $o]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y2) => 237.26/35.00 (( 237.26/35.00 !!(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 Y0) => 237.26/35.00 (Y1(Y3) => 237.26/35.00 (Y3 = Y2)))))) => 237.26/35.00 (??(( 237.26/35.00 ^[Y3 : $i]: 237.26/35.00 (in(Y3, 237.26/35.00 dsetconstr( 237.26/35.00 Y0, Y1)) & 237.26/35.00 (dsetconstr( 237.26/35.00 Y0, Y1) = 237.26/35.00 setadjoin( 237.26/35.00 Y3, 237.26/35.00 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.00 inference('lazy_cnf_imply', [status(thm)], ['235'])). 237.26/35.00 tff('237', plain, 237.26/35.00 ~ ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => (powerset(Y0) = powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 ((??((^[Y1 : $i]: 237.26/35.00 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i > $o]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 ((!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $i]: 237.26/35.00 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y0(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 ((??((^[Y2 : $i]: 237.26/35.00 (Y1(Y2) & 237.26/35.00 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.00 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((Y0 = Y1) => 237.26/35.00 (!!((^[Y2 : $i > $o]: 237.26/35.00 (!!((^[Y3 : $i > $o]: 237.26/35.00 ((!!((^[Y4 : $i]: 237.26/35.00 (in(Y4, Y0) => 237.26/35.00 (!!((^[Y5 : $i]: 237.26/35.00 (in(Y5, Y1) => 237.26/35.00 ((Y4 = Y5) => 237.26/35.00 (Y2(Y4) <=> Y3(Y5))))))))))) => 237.26/35.00 (dsetconstr(Y0, Y2) = 237.26/35.00 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.00 subset(Y0, Y1)))))))) => 237.26/35.00 ((!!(subset(emptyset))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => 237.26/35.00 (~(subset(Y0, Y1)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y2) => 237.26/35.00 subset(Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y0, Y2) => 237.26/35.00 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 in(Y0, powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y1, Y0) => 237.26/35.00 in(Y1, powerset(Y0))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (in(Y1, powerset(Y0)) => 237.26/35.00 subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 subset(powerset(Y0), 237.26/35.00 powerset(Y1))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 in(dsetconstr(Y0, Y1), 237.26/35.00 powerset(Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i > $o]: 237.26/35.00 subset(dsetconstr(Y0, Y1), 237.26/35.00 Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 in(Y1, 237.26/35.00 setadjoin(Y0, 237.26/35.00 setadjoin(Y1, emptyset))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binunion(Y0, Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (!!((^[Y3 : $o]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (( 237.26/35.00 in(Y2, 237.26/35.00 Y0) => Y3) => 237.26/35.00 ( 237.26/35.00 ( 237.26/35.00 in(Y2, 237.26/35.00 Y1) => Y3) => 237.26/35.00 Y3))))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binunion(Y0, 237.26/35.00 Y1)) => 237.26/35.00 (in(Y2, Y1) | 237.26/35.00 in(Y2, Y0)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y0, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset(Y1, 237.26/35.00 binunion(Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, Y0) => 237.26/35.00 (in(Y2, Y1) => 237.26/35.00 in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (subset(Y2, 237.26/35.00 Y0) => 237.26/35.00 (subset(Y2, 237.26/35.00 Y1) => 237.26/35.00 subset(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), Y0))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y0, Y1) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1) => 237.26/35.00 subset(Y1, Y0)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!((^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((~((??(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) & 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 subset( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 Y1))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (subset(Y1, 237.26/35.00 Y0) => 237.26/35.00 (binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ((binintersect( 237.26/35.00 Y0, Y1) = 237.26/35.00 Y0) => 237.26/35.00 subset( 237.26/35.00 Y0, Y1)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (binintersect( 237.26/35.00 Y0, 237.26/35.00 binunion( 237.26/35.00 Y1, Y2)) = 237.26/35.00 binunion( 237.26/35.00 binintersect( 237.26/35.00 Y0, Y1), 237.26/35.00 binintersect( 237.26/35.00 Y0, Y2)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 in(Y2, 237.26/35.00 Y0))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!((^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (subset( 237.26/35.00 Y0, Y1) => 237.26/35.00 ( 237.26/35.00 setminus( 237.26/35.00 Y0, Y1) = 237.26/35.00 emptyset)))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 ( 237.26/35.00 !!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (in(Y2, 237.26/35.00 Y0) => 237.26/35.00 in(Y2, 237.26/35.00 Y1)))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 setminus( 237.26/35.00 Y0, Y1)))) => 237.26/35.00 (( 237.26/35.00 ~( 237.26/35.00 in(Y2, 237.26/35.00 Y1))) => 237.26/35.00 (~( 237.26/35.00 in(Y2, 237.26/35.00 Y0)))))))))))))) => 237.26/35.00 ((!!((^[Y0 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y1 : $i]: 237.26/35.00 (!!(( 237.26/35.00 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset) => 237.26/35.01 subset( 237.26/35.01 Y0, Y1)))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $o]: 237.26/35.01 (( 237.26/35.01 in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 Y3)) => 237.26/35.01 (( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y1) => Y3)) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 Y0)))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 Y0))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))) => 237.26/35.01 (( 237.26/35.01 Y2 = Y1) | 237.26/35.01 (Y2 = Y0)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 Y1) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 setunion( 237.26/35.01 Y0)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y1, 237.26/35.01 Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)), 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)) = 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y2 = Y3))))))))))) => 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y3 = Y2)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.01 inference('lazy_cnf_imply', [status(thm)], ['236'])). 237.26/35.01 tff('238', plain, 237.26/35.01 ~ ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((Y0 = Y1) => (setunion(Y0) = setunion(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i > $o]: 237.26/35.01 ((??((^[Y1 : $i]: 237.26/35.01 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i > $o]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 ((!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $i]: 237.26/35.01 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.01 ((??((^[Y2 : $i]: 237.26/35.01 (Y0(Y2) & 237.26/35.01 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.01 ((??((^[Y2 : $i]: 237.26/35.01 (Y1(Y2) & 237.26/35.01 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.01 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((Y0 = Y1) => 237.26/35.01 (!!((^[Y2 : $i > $o]: 237.26/35.01 (!!((^[Y3 : $i > $o]: 237.26/35.01 ((!!((^[Y4 : $i]: 237.26/35.01 (in(Y4, Y0) => 237.26/35.01 (!!((^[Y5 : $i]: 237.26/35.01 (in(Y5, Y1) => 237.26/35.01 ((Y4 = Y5) => 237.26/35.01 (Y2(Y4) <=> Y3(Y5))))))))))) => 237.26/35.01 (dsetconstr(Y0, Y2) = 237.26/35.01 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!(subset(emptyset))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => 237.26/35.01 (~(subset(Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y2) => 237.26/35.01 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 in(Y0, powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => 237.26/35.01 in(Y1, powerset(Y0))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (in(Y1, powerset(Y0)) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 subset(powerset(Y0), 237.26/35.01 powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 in(dsetconstr(Y0, Y1), 237.26/35.01 powerset(Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin(Y0, 237.26/35.01 setadjoin(Y1, emptyset))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $o]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)) => 237.26/35.01 ((in(Y2, 237.26/35.01 Y0) => Y3) => 237.26/35.01 (( 237.26/35.01 in(Y2, 237.26/35.01 Y1) => Y3) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion(Y0, 237.26/35.01 Y1)) => 237.26/35.01 (in(Y2, Y1) | 237.26/35.01 in(Y2, Y0)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y0, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y1, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y2, 237.26/35.01 Y0) => 237.26/35.01 (subset(Y2, 237.26/35.01 Y1) => 237.26/35.01 subset(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect(Y0, 237.26/35.01 Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y1) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((~((??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), 237.26/35.01 Y1))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, 237.26/35.01 Y0) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y0) => 237.26/35.01 subset(Y0, 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (binintersect( 237.26/35.01 Y0, 237.26/35.01 binunion( 237.26/35.01 Y1, Y2)) = 237.26/35.01 binunion( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), 237.26/35.01 binintersect( 237.26/35.01 Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, 237.26/35.01 Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset( 237.26/35.01 Y0, Y1) => 237.26/35.01 (setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in(Y2, 237.26/35.01 Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset) => 237.26/35.01 subset( 237.26/35.01 Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $o]: 237.26/35.01 (( 237.26/35.01 in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 Y3)) => 237.26/35.01 (( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y1) => Y3)) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 Y0)))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 Y0))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))) => 237.26/35.01 (( 237.26/35.01 Y2 = Y1) | 237.26/35.01 (Y2 = Y0)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 Y1) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 setunion( 237.26/35.01 Y0)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y1, 237.26/35.01 Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)), 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)) = 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y2 = Y3))))))))))) => 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y3 = Y2)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.01 inference('lazy_cnf_imply', [status(thm)], ['237'])). 237.26/35.01 tff('239', plain, 237.26/35.01 ~ ((!!((^[Y0 : $i > $o]: 237.26/35.01 ((??((^[Y1 : $i]: 237.26/35.01 (Y0(Y1) & (!!((^[Y2 : $i]: (Y0(Y2) => (Y1 = Y2))))))))) => 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i > $o]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 ((!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $i]: 237.26/35.01 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.01 ((??((^[Y2 : $i]: 237.26/35.01 (Y0(Y2) & 237.26/35.01 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.01 ((??((^[Y2 : $i]: 237.26/35.01 (Y1(Y2) & 237.26/35.01 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.01 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((Y0 = Y1) => 237.26/35.01 (!!((^[Y2 : $i > $o]: 237.26/35.01 (!!((^[Y3 : $i > $o]: 237.26/35.01 ((!!((^[Y4 : $i]: 237.26/35.01 (in(Y4, Y0) => 237.26/35.01 (!!((^[Y5 : $i]: 237.26/35.01 (in(Y5, Y1) => 237.26/35.01 ((Y4 = Y5) => 237.26/35.01 (Y2(Y4) <=> Y3(Y5))))))))))) => 237.26/35.01 (dsetconstr(Y0, Y2) = 237.26/35.01 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!(subset(emptyset))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => 237.26/35.01 (~(subset(Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y2) => 237.26/35.01 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => 237.26/35.01 in(Y1, powerset(Y0))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (in(Y1, powerset(Y0)) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 subset(powerset(Y0), 237.26/35.01 powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 in(dsetconstr(Y0, Y1), 237.26/35.01 powerset(Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin(Y0, 237.26/35.01 setadjoin(Y1, emptyset))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $o]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)) => 237.26/35.01 ((in(Y2, Y0) => 237.26/35.01 Y3) => 237.26/35.01 ((in(Y2, 237.26/35.01 Y1) => Y3) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion(Y0, Y1)) => 237.26/35.01 (in(Y2, Y1) | 237.26/35.01 in(Y2, Y0)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y0, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y1, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y2, Y0) => 237.26/35.01 (subset(Y2, 237.26/35.01 Y1) => 237.26/35.01 subset(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect(Y0, 237.26/35.01 Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (binintersect(Y0, 237.26/35.01 Y1) = 237.26/35.01 Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y1) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((~((??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), 237.26/35.01 Y1))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, 237.26/35.01 Y0) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y0) => 237.26/35.01 subset(Y0, 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 ( 237.26/35.01 binintersect( 237.26/35.01 Y0, 237.26/35.01 binunion( 237.26/35.01 Y1, Y2)) = 237.26/35.01 binunion( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), 237.26/35.01 binintersect( 237.26/35.01 Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, 237.26/35.01 Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset( 237.26/35.01 Y0, Y1) => 237.26/35.01 (setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in(Y2, 237.26/35.01 Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset) => 237.26/35.01 subset( 237.26/35.01 Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $o]: 237.26/35.01 (( 237.26/35.01 in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 Y3)) => 237.26/35.01 (( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y1) => Y3)) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))))))))) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 Y0)))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 Y0))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))) => 237.26/35.01 (( 237.26/35.01 Y2 = Y1) | 237.26/35.01 (Y2 = Y0)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 Y1) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 setunion( 237.26/35.01 Y0)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y1, 237.26/35.01 Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)), 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)) = 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y2 = Y3))))))))))) => 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y3 = Y2)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.01 inference('lazy_cnf_imply', [status(thm)], ['238'])). 237.26/35.01 tff('240', plain, 237.26/35.01 ~ ((!!((^[Y0 : $i > $o]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 ((!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $i]: 237.26/35.01 ((Y2 = Y3) => (Y0(Y2) <=> Y1(Y3))))))))) => 237.26/35.01 ((??((^[Y2 : $i]: 237.26/35.01 (Y0(Y2) & 237.26/35.01 (!!((^[Y3 : $i]: (Y0(Y3) => (Y2 = Y3))))))))) => 237.26/35.01 ((??((^[Y2 : $i]: 237.26/35.01 (Y1(Y2) & 237.26/35.01 (!!((^[Y3 : $i]: (Y1(Y3) => (Y2 = Y3))))))))) => 237.26/35.01 (descr(Y0) = descr(Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((Y0 = Y1) => 237.26/35.01 (!!((^[Y2 : $i > $o]: 237.26/35.01 (!!((^[Y3 : $i > $o]: 237.26/35.01 ((!!((^[Y4 : $i]: 237.26/35.01 (in(Y4, Y0) => 237.26/35.01 (!!((^[Y5 : $i]: 237.26/35.01 (in(Y5, Y1) => 237.26/35.01 ((Y4 = Y5) => 237.26/35.01 (Y2(Y4) <=> Y3(Y5))))))))))) => 237.26/35.01 (dsetconstr(Y0, Y2) = 237.26/35.01 dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!(subset(emptyset))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y2) => 237.26/35.01 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => 237.26/35.01 in(Y1, powerset(Y0))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (in(Y1, powerset(Y0)) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 subset(powerset(Y0), 237.26/35.01 powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 in(dsetconstr(Y0, Y1), 237.26/35.01 powerset(Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin(Y0, 237.26/35.01 setadjoin(Y1, emptyset))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $o]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)) => 237.26/35.01 ((in(Y2, Y0) => 237.26/35.01 Y3) => 237.26/35.01 ((in(Y2, Y1) => 237.26/35.01 Y3) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion(Y0, Y1)) => 237.26/35.01 (in(Y2, Y1) | 237.26/35.01 in(Y2, Y0)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y0, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y1, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y2, Y0) => 237.26/35.01 (subset(Y2, Y1) => 237.26/35.01 subset(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect(Y0, 237.26/35.01 Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (binintersect(Y0, 237.26/35.01 Y1) = 237.26/35.01 Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect(Y0, 237.26/35.01 Y1) = 237.26/35.01 Y1) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((~((??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), Y1))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y0) => 237.26/35.01 subset(Y0, 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (binintersect( 237.26/35.01 Y0, 237.26/35.01 binunion( 237.26/35.01 Y1, Y2)) = 237.26/35.01 binunion( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), 237.26/35.01 binintersect( 237.26/35.01 Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, 237.26/35.01 Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 subset( 237.26/35.01 Y0, Y1) => 237.26/35.01 ( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in(Y2, 237.26/35.01 Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset) => 237.26/35.01 subset( 237.26/35.01 Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $o]: 237.26/35.01 (( 237.26/35.01 in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 Y3)) => 237.26/35.01 (( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y1) => Y3)) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 Y0)))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 Y0))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))) => 237.26/35.01 (( 237.26/35.01 Y2 = Y1) | 237.26/35.01 (Y2 = Y0)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 Y1) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 setunion( 237.26/35.01 Y0)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y1, 237.26/35.01 Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)), 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)) = 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y2 = Y3))))))))))) => 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y3 = Y2)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.01 inference('lazy_cnf_imply', [status(thm)], ['239'])). 237.26/35.01 tff('241', plain, 237.26/35.01 ~ ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((Y0 = Y1) => 237.26/35.01 (!!((^[Y2 : $i > $o]: 237.26/35.01 (!!((^[Y3 : $i > $o]: 237.26/35.01 ((!!((^[Y4 : $i]: 237.26/35.01 (in(Y4, Y0) => 237.26/35.01 (!!((^[Y5 : $i]: 237.26/35.01 (in(Y5, Y1) => 237.26/35.01 ((Y4 = Y5) => 237.26/35.01 (Y2(Y4) <=> Y3(Y5))))))))))) => 237.26/35.01 (dsetconstr(Y0, Y2) = dsetconstr(Y1, Y3)))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!(subset(emptyset))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y2) => 237.26/35.01 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => 237.26/35.01 in(Y1, powerset(Y0))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (in(Y1, powerset(Y0)) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 in(dsetconstr(Y0, Y1), 237.26/35.01 powerset(Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin(Y0, 237.26/35.01 setadjoin(Y1, emptyset))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $o]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)) => 237.26/35.01 ((in(Y2, Y0) => 237.26/35.01 Y3) => 237.26/35.01 ((in(Y2, Y1) => 237.26/35.01 Y3) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion(Y0, Y1)) => 237.26/35.01 (in(Y2, Y1) | 237.26/35.01 in(Y2, Y0)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y0, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y1, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y2, Y0) => 237.26/35.01 (subset(Y2, Y1) => 237.26/35.01 subset(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect(Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (binintersect(Y0, 237.26/35.01 Y1) = 237.26/35.01 Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect(Y0, 237.26/35.01 Y1) = 237.26/35.01 Y1) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((~((??((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), Y1))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y0) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (binintersect( 237.26/35.01 Y0, 237.26/35.01 binunion( 237.26/35.01 Y1, Y2)) = 237.26/35.01 binunion( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), 237.26/35.01 binintersect( 237.26/35.01 Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, 237.26/35.01 Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset( 237.26/35.01 Y0, Y1) => 237.26/35.01 ( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in(Y2, 237.26/35.01 Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset) => 237.26/35.01 subset( 237.26/35.01 Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $o]: 237.26/35.01 (( 237.26/35.01 in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 Y3)) => 237.26/35.01 (( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y1) => Y3)) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 Y0)))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 Y0))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))) => 237.26/35.01 (( 237.26/35.01 Y2 = Y1) | 237.26/35.01 (Y2 = Y0)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 subset( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 powerset( 237.26/35.01 powerset( 237.26/35.01 binunion( 237.26/35.01 Y0, Y1)))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y1) => 237.26/35.01 in( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)), 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 Y1) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 cartprod( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (??(( 237.26/35.01 ^[Y4 : $i]: 237.26/35.01 (in(Y4, 237.26/35.01 setunion( 237.26/35.01 Y2)) & 237.26/35.01 (Y2 = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 setadjoin( 237.26/35.01 Y4, 237.26/35.01 emptyset)), 237.26/35.01 emptyset))))))))))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (in(Y1, 237.26/35.01 setunion( 237.26/35.01 Y0)) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y1, 237.26/35.01 Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)), 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 subset( 237.26/35.01 Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (setunion( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset)) = 237.26/35.01 Y0)))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y2 = Y3))))))))))) => 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))))))))))) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (( 237.26/35.01 ??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 Y1(Y2)))))))))))) => 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i > $o]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y2) => 237.26/35.01 (( 237.26/35.01 !!(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 Y0) => 237.26/35.01 (Y1(Y3) => 237.26/35.01 (Y3 = Y2)))))) => 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 dsetconstr( 237.26/35.01 Y0, Y1)) & 237.26/35.01 (dsetconstr( 237.26/35.01 Y0, Y1) = 237.26/35.01 setadjoin( 237.26/35.01 Y3, 237.26/35.01 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.01 inference('lazy_cnf_imply', [status(thm)], ['240'])). 237.26/35.01 tff('242', plain, 237.26/35.01 ~ ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!(subset(emptyset))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y0, Y2) => 237.26/35.01 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (in(Y1, powerset(Y0)) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 in(dsetconstr(Y0, Y1), 237.26/35.01 powerset(Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i > $o]: 237.26/35.01 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin(Y0, 237.26/35.01 setadjoin(Y1, emptyset))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binunion(Y0, Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (!!((^[Y3 : $o]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion(Y0, 237.26/35.01 Y1)) => 237.26/35.01 ((in(Y2, Y0) => 237.26/35.01 Y3) => 237.26/35.01 ((in(Y2, Y1) => 237.26/35.01 Y3) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binunion(Y0, Y1)) => 237.26/35.01 (in(Y2, Y1) | 237.26/35.01 in(Y2, Y0)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y0, binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset(Y1, 237.26/35.01 binunion(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, Y0) => 237.26/35.01 (in(Y2, Y1) => 237.26/35.01 in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (subset(Y2, Y0) => 237.26/35.01 (subset(Y2, Y1) => 237.26/35.01 subset(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect(Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y0, Y1) => 237.26/35.01 (binintersect(Y0, Y1) = 237.26/35.01 Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect(Y0, 237.26/35.01 Y1) = 237.26/35.01 Y1) => 237.26/35.01 subset(Y1, Y0)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, Y1))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((~((??((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) & 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))) => 237.26/35.01 (binintersect(Y0, 237.26/35.01 Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), Y1))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset(Y1, Y0) => 237.26/35.01 (binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ((binintersect( 237.26/35.01 Y0, Y1) = 237.26/35.01 Y0) => 237.26/35.01 subset(Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (binintersect( 237.26/35.01 Y0, 237.26/35.01 binunion( 237.26/35.01 Y1, Y2)) = 237.26/35.01 binunion( 237.26/35.01 binintersect( 237.26/35.01 Y0, Y1), 237.26/35.01 binintersect( 237.26/35.01 Y0, Y2)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!((^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 in(Y2, 237.26/35.01 Y0))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)) => 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (subset( 237.26/35.01 Y0, Y1) => 237.26/35.01 (setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 in(Y2, 237.26/35.01 Y1)))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 Y0)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!((^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 setminus( 237.26/35.01 Y0, Y1)))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 subset( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1), 237.26/35.01 Y0))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 setminus( 237.26/35.01 Y0, Y1) = 237.26/35.01 emptyset) => 237.26/35.01 subset( 237.26/35.01 Y0, Y1)))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1)) => 237.26/35.01 (!!(( 237.26/35.01 ^[Y3 : $o]: 237.26/35.01 (( 237.26/35.01 in(Y2, 237.26/35.01 Y0) => 237.26/35.01 ( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 Y3)) => 237.26/35.01 (( 237.26/35.01 ( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 ( 237.26/35.01 in(Y2, 237.26/35.01 Y1) => Y3)) => 237.26/35.01 Y3))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 Y0) => 237.26/35.01 (in(Y2, 237.26/35.01 Y1) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!((^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y0))) => 237.26/35.01 (( 237.26/35.01 ~( 237.26/35.01 in(Y2, 237.26/35.01 Y1))) => 237.26/35.01 (~( 237.26/35.01 in(Y2, 237.26/35.01 symdiff( 237.26/35.01 Y0, Y1))))))))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 ( 237.26/35.01 !!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y0, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 in(Y1, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))))))))) => 237.26/35.01 ((!!(( 237.26/35.01 ^[Y0 : $i]: 237.26/35.01 (!!(( 237.26/35.01 ^[Y1 : $i]: 237.26/35.01 (??(( 237.26/35.01 ^[Y2 : $i]: 237.26/35.01 (in(Y2, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (??(( 237.26/35.01 ^[Y3 : $i]: 237.26/35.01 (in(Y3, 237.26/35.01 setunion( 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)))) & 237.26/35.01 (setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 emptyset), 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y0, 237.26/35.01 setadjoin( 237.26/35.01 Y1, 237.26/35.01 emptyset)), 237.26/35.01 emptyset)) = 237.26/35.01 setadjoin( 237.26/35.01 setadjoin( 237.26/35.01 Y2, 237.26/35.01 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 Y0)))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 Y0))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))) => 237.26/35.02 (( 237.26/35.02 Y2 = Y1) | 237.26/35.02 (Y2 = Y0)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 Y1) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 setunion( 237.26/35.02 Y0)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y1, 237.26/35.02 Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)), 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)) = 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y2 = Y3))))))))))) => 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y3 = Y2)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.02 inference('lazy_cnf_imply', [status(thm)], ['241'])). 237.26/35.02 tff('243', plain, 237.26/35.02 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!(subset(emptyset))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y2) => 237.26/35.02 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin(Y0, 237.26/35.02 setadjoin(Y1, emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (!!((^[Y3 : $o]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, 237.26/35.02 Y1)) => 237.26/35.02 ((in(Y2, Y0) => 237.26/35.02 Y3) => 237.26/35.02 ((in(Y2, Y1) => 237.26/35.02 Y3) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, Y1)) => 237.26/35.02 (in(Y2, Y1) | 237.26/35.02 in(Y2, Y0)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y0, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y1, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y2, Y0) => 237.26/35.02 (subset(Y2, Y1) => 237.26/35.02 subset(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, Y1) = 237.26/35.02 Y1) => 237.26/35.02 subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y1))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((~((??((^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y2, 237.26/35.02 Y1))))))) => 237.26/35.02 (binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1), Y1))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => 237.26/35.02 (binintersect( 237.26/35.02 Y0, Y1) = 237.26/35.02 Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect( 237.26/35.02 Y0, Y1) = 237.26/35.02 Y0) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 binintersect( 237.26/35.02 Y0, 237.26/35.02 binunion( 237.26/35.02 Y1, Y2)) = 237.26/35.02 binunion( 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1), 237.26/35.02 binintersect( 237.26/35.02 Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, 237.26/35.02 Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, 237.26/35.02 Y1) => 237.26/35.02 (setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in(Y2, 237.26/35.02 Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset) => 237.26/35.02 subset( 237.26/35.02 Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $o]: 237.26/35.02 (( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 Y3)) => 237.26/35.02 (( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y1) => Y3)) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 Y0)))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 Y0))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))) => 237.26/35.02 (( 237.26/35.02 Y2 = Y1) | 237.26/35.02 (Y2 = Y0)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 Y1) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 setunion( 237.26/35.02 Y0)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y1, 237.26/35.02 Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)), 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)) = 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y2 = Y3))))))))))) => 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y3 = Y2)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.02 inference('lazy_cnf_imply', [status(thm)], ['242'])). 237.26/35.02 tff('244', plain, 237.26/35.02 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: ((Y0 = Y1) => subset(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!(subset(emptyset))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y2) => 237.26/35.02 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin(Y0, 237.26/35.02 setadjoin(Y1, emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (!!((^[Y3 : $o]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, 237.26/35.02 Y1)) => 237.26/35.02 ((in(Y2, Y0) => 237.26/35.02 Y3) => 237.26/35.02 ((in(Y2, Y1) => 237.26/35.02 Y3) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, Y1)) => 237.26/35.02 (in(Y2, Y1) | 237.26/35.02 in(Y2, Y0)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y0, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y1, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y2, Y0) => 237.26/35.02 (subset(Y2, Y1) => 237.26/35.02 subset(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, Y1) = 237.26/35.02 Y1) => 237.26/35.02 subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y1))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((~((??((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y2, 237.26/35.02 Y1))))))) => 237.26/35.02 (binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1), Y1))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => 237.26/35.02 (binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect( 237.26/35.02 Y0, Y1) = 237.26/35.02 Y0) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (binintersect( 237.26/35.02 Y0, 237.26/35.02 binunion( 237.26/35.02 Y1, Y2)) = 237.26/35.02 binunion( 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1), 237.26/35.02 binintersect( 237.26/35.02 Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, 237.26/35.02 Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, 237.26/35.02 Y1) => 237.26/35.02 (setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in(Y2, 237.26/35.02 Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset) => 237.26/35.02 subset( 237.26/35.02 Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $o]: 237.26/35.02 (( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 Y3)) => 237.26/35.02 (( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y1) => Y3)) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 Y0)))))))) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 Y0))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))) => 237.26/35.02 (( 237.26/35.02 Y2 = Y1) | 237.26/35.02 (Y2 = Y0)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 Y1) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 setunion( 237.26/35.02 Y0)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y1, 237.26/35.02 Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)), 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)) = 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y2 = Y3))))))))))) => 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y3 = Y2)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.02 inference('lazy_cnf_imply', [status(thm)], ['243'])). 237.26/35.02 tff('245', plain, 237.26/35.02 ~ ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((!!((^[Y2 : $i]: (in(Y2, Y0) => in(Y2, Y1))))) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!(subset(emptyset))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y2) => 237.26/35.02 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin(Y0, 237.26/35.02 setadjoin(Y1, emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (!!((^[Y3 : $o]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, Y1)) => 237.26/35.02 ((in(Y2, Y0) => Y3) => 237.26/35.02 ((in(Y2, Y1) => 237.26/35.02 Y3) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, binunion(Y0, Y1)) => 237.26/35.02 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y0, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y1, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y2, Y0) => 237.26/35.02 (subset(Y2, Y1) => 237.26/35.02 subset(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1)) => 237.26/35.02 in(Y2, Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, Y1) = 237.26/35.02 Y1) => 237.26/35.02 subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y1))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((~((??((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) & 237.26/35.02 in(Y2, Y1))))))) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1), Y1))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => 237.26/35.02 (binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 Y0) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (binintersect( 237.26/35.02 Y0, 237.26/35.02 binunion( 237.26/35.02 Y1, Y2)) = 237.26/35.02 binunion( 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1), 237.26/35.02 binintersect( 237.26/35.02 Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, 237.26/35.02 Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, 237.26/35.02 Y1) => 237.26/35.02 (setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in(Y2, 237.26/35.02 Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset) => 237.26/35.02 subset( 237.26/35.02 Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $o]: 237.26/35.02 (( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 Y3)) => 237.26/35.02 (( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y1) => Y3)) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 Y0)))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 Y0))))))))) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))) => 237.26/35.02 (( 237.26/35.02 Y2 = Y1) | 237.26/35.02 (Y2 = Y0)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 Y1) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 setunion( 237.26/35.02 Y0)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y1, 237.26/35.02 Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)), 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)) = 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y2 = Y3))))))))))) => 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y3 = Y2)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.02 inference('lazy_cnf_imply', [status(thm)], ['244'])). 237.26/35.02 tff('246', plain, 237.26/35.02 ~ ((!!(subset(emptyset))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y2) => 237.26/35.02 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin(Y0, 237.26/35.02 setadjoin(Y1, emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (!!((^[Y3 : $o]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, Y1)) => 237.26/35.02 ((in(Y2, Y0) => Y3) => 237.26/35.02 ((in(Y2, Y1) => Y3) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, binunion(Y0, Y1)) => 237.26/35.02 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y0, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y1, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y2, Y0) => 237.26/35.02 (subset(Y2, Y1) => 237.26/35.02 subset(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1)) => 237.26/35.02 in(Y2, Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, Y1) = 237.26/35.02 Y1) => 237.26/35.02 subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y1))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((~((??((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) & 237.26/35.02 in(Y2, Y1))))))) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, Y1), 237.26/35.02 Y1))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => 237.26/35.02 (binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 Y0) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (binintersect( 237.26/35.02 Y0, 237.26/35.02 binunion( 237.26/35.02 Y1, Y2)) = 237.26/35.02 binunion( 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1), 237.26/35.02 binintersect( 237.26/35.02 Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, 237.26/35.02 Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (setminus(Y0, 237.26/35.02 Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in(Y2, 237.26/35.02 Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset) => 237.26/35.02 subset( 237.26/35.02 Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $o]: 237.26/35.02 (( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 Y3)) => 237.26/35.02 (( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y1) => Y3)) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 Y0)))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 Y0))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))) => 237.26/35.02 (( 237.26/35.02 Y2 = Y1) | 237.26/35.02 (Y2 = Y0)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 Y1) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 setunion( 237.26/35.02 Y0)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y1, 237.26/35.02 Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)), 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)) = 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y2 = Y3))))))))))) => 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y3 = Y2)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.02 inference('lazy_cnf_imply', [status(thm)], ['245'])). 237.26/35.02 tff('247', plain, 237.26/35.02 ~ ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y2) => 237.26/35.02 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin(Y0, 237.26/35.02 setadjoin(Y1, emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (!!((^[Y3 : $o]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, Y1)) => 237.26/35.02 ((in(Y2, Y0) => Y3) => 237.26/35.02 ((in(Y2, Y1) => Y3) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, binunion(Y0, Y1)) => 237.26/35.02 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y0, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y1, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, 237.26/35.02 binintersect(Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y2, Y0) => 237.26/35.02 (subset(Y2, Y1) => 237.26/35.02 subset(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect(Y0, 237.26/35.02 Y1)) => 237.26/35.02 in(Y2, Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (binintersect(Y0, Y1) = Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, Y1) = 237.26/35.02 Y1) => 237.26/35.02 subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y1))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((~((??((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) & 237.26/35.02 in(Y2, Y1))))))) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 binintersect(Y0, Y1), 237.26/35.02 Y1))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => 237.26/35.02 (binintersect(Y0, Y1) = 237.26/35.02 Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ((binintersect(Y0, 237.26/35.02 Y1) = 237.26/35.02 Y0) => 237.26/35.02 subset(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (binintersect( 237.26/35.02 Y0, 237.26/35.02 binunion( 237.26/35.02 Y1, Y2)) = 237.26/35.02 binunion( 237.26/35.02 binintersect( 237.26/35.02 Y0, Y1), 237.26/35.02 binintersect( 237.26/35.02 Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 in(Y2, Y0))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (setminus(Y0, 237.26/35.02 Y1) = 237.26/35.02 emptyset)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in(Y2, 237.26/35.02 Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y1) => 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 setminus( 237.26/35.02 Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1), 237.26/35.02 Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (( 237.26/35.02 setminus( 237.26/35.02 Y0, Y1) = 237.26/35.02 emptyset) => 237.26/35.02 subset( 237.26/35.02 Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $o]: 237.26/35.02 (( 237.26/35.02 in(Y2, 237.26/35.02 Y0) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 Y3)) => 237.26/35.02 (( 237.26/35.02 ( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 ( 237.26/35.02 in(Y2, 237.26/35.02 Y1) => Y3)) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (in(Y2, 237.26/35.02 Y1) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y0))) => 237.26/35.02 (( 237.26/35.02 ~( 237.26/35.02 in(Y2, 237.26/35.02 Y1))) => 237.26/35.02 (~( 237.26/35.02 in(Y2, 237.26/35.02 symdiff( 237.26/35.02 Y0, Y1))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)))) & 237.26/35.02 (setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)) = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 Y0)))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 Y0))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))) => 237.26/35.02 ((!!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 setadjoin( 237.26/35.02 Y1, 237.26/35.02 emptyset))) => 237.26/35.02 (( 237.26/35.02 Y2 = Y1) | 237.26/35.02 (Y2 = Y0)))))))))))) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 subset( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 powerset( 237.26/35.02 powerset( 237.26/35.02 binunion( 237.26/35.02 Y0, Y1)))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y1) => 237.26/35.02 in( 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset)), 237.26/35.02 emptyset)), 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 Y1) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 cartprod( 237.26/35.02 Y0, Y1)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (??(( 237.26/35.02 ^[Y4 : $i]: 237.26/35.02 (in(Y4, 237.26/35.02 setunion( 237.26/35.02 Y2)) & 237.26/35.02 (Y2 = 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset), 237.26/35.02 setadjoin( 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 setadjoin( 237.26/35.02 Y4, 237.26/35.02 emptyset)), 237.26/35.02 emptyset))))))))))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i]: 237.26/35.02 (in(Y1, 237.26/35.02 setunion( 237.26/35.02 Y0)) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 in(Y1, 237.26/35.02 Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)), 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 subset( 237.26/35.02 Y0, 237.26/35.02 setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (setunion( 237.26/35.02 setadjoin( 237.26/35.02 Y0, 237.26/35.02 emptyset)) = 237.26/35.02 Y0)))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (!!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y2 = Y3))))))))))) => 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))))))))))) => 237.26/35.02 ( 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (( 237.26/35.02 ??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y2, 237.26/35.02 emptyset)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) & 237.26/35.02 Y1(Y2)))))))))))) => 237.26/35.02 ( 237.26/35.02 !!(( 237.26/35.02 ^[Y0 : $i]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y1 : $i > $o]: 237.26/35.02 (!!(( 237.26/35.02 ^[Y2 : $i]: 237.26/35.02 (in(Y2, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y2) => 237.26/35.02 (( 237.26/35.02 !!(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 Y0) => 237.26/35.02 (Y1(Y3) => 237.26/35.02 (Y3 = Y2)))))) => 237.26/35.02 (??(( 237.26/35.02 ^[Y3 : $i]: 237.26/35.02 (in(Y3, 237.26/35.02 dsetconstr( 237.26/35.02 Y0, Y1)) & 237.26/35.02 (dsetconstr( 237.26/35.02 Y0, Y1) = 237.26/35.02 setadjoin( 237.26/35.02 Y3, 237.26/35.02 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.26/35.02 inference('lazy_cnf_imply', [status(thm)], ['246'])). 237.26/35.02 tff('248', plain, 237.26/35.02 ~ ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y0, Y2) => 237.26/35.02 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (subset(Y0, Y1) => 237.26/35.02 subset(powerset(Y0), powerset(Y1))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i > $o]: 237.26/35.02 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 in(Y1, 237.26/35.02 setadjoin(Y0, 237.26/35.02 setadjoin(Y1, emptyset))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, binunion(Y0, Y1)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (!!((^[Y3 : $o]: 237.26/35.02 (in(Y2, 237.26/35.02 binunion(Y0, Y1)) => 237.26/35.02 ((in(Y2, Y0) => Y3) => 237.26/35.02 ((in(Y2, Y1) => Y3) => 237.26/35.02 Y3))))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, binunion(Y0, Y1)) => 237.26/35.02 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y0, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 subset(Y1, binunion(Y0, Y1)))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (in(Y2, Y0) => 237.26/35.02 (in(Y2, Y1) => 237.26/35.02 in(Y2, 237.26/35.02 binintersect(Y0, Y1))))))))))))) => 237.26/35.02 ((!!((^[Y0 : $i]: 237.26/35.02 (!!((^[Y1 : $i]: 237.26/35.02 (!!((^[Y2 : $i]: 237.26/35.02 (subset(Y2, Y0) => 237.26/35.02 (subset(Y2, Y1) => 237.26/35.02 subset(Y2, 237.26/35.03 binintersect(Y0, Y1))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 binintersect(Y0, Y1)) => 237.26/35.03 in(Y2, Y0))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 subset(binintersect(Y0, Y1), 237.26/35.03 Y0))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (subset(Y0, Y1) => 237.26/35.03 (binintersect(Y0, Y1) = Y0)))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 ((binintersect(Y0, Y1) = Y1) => 237.26/35.03 subset(Y1, Y0)))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 binintersect( 237.26/35.03 Y0, Y1)) => 237.26/35.03 in(Y2, Y1))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 ((~((??((^[Y2 : $i]: 237.26/35.03 (in(Y2, Y0) & 237.26/35.03 in(Y2, Y1))))))) => 237.26/35.03 (binintersect(Y0, Y1) = 237.26/35.03 emptyset)))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 subset( 237.26/35.03 binintersect(Y0, Y1), 237.26/35.03 Y1))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (subset(Y1, Y0) => 237.26/35.03 (binintersect(Y0, Y1) = 237.26/35.03 Y1)))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 ((binintersect(Y0, Y1) = 237.26/35.03 Y0) => 237.26/35.03 subset(Y0, Y1)))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (binintersect( 237.26/35.03 Y0, 237.26/35.03 binunion( 237.26/35.03 Y1, Y2)) = 237.26/35.03 binunion( 237.26/35.03 binintersect( 237.26/35.03 Y0, Y1), 237.26/35.03 binintersect( 237.26/35.03 Y0, Y2)))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (in(Y2, Y0) => 237.26/35.03 ((~( 237.26/35.03 in(Y2, Y1))) => 237.26/35.03 in(Y2, 237.26/35.03 setminus( 237.26/35.03 Y0, Y1))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 setminus( 237.26/35.03 Y0, Y1)) => 237.26/35.03 in(Y2, Y0))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 setminus( 237.26/35.03 Y0, Y1)) => 237.26/35.03 (~( 237.26/35.03 in(Y2, 237.26/35.03 Y1))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (subset(Y0, Y1) => 237.26/35.03 (setminus(Y0, 237.26/35.03 Y1) = 237.26/35.03 emptyset)))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 ( 237.26/35.03 ( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 setminus( 237.26/35.03 Y0, Y1)))) => 237.26/35.03 ( 237.26/35.03 in(Y2, 237.26/35.03 Y0) => 237.26/35.03 in(Y2, 237.26/35.03 Y1)))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 setminus( 237.26/35.03 Y0, Y1)))) => 237.26/35.03 (( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y1))) => 237.26/35.03 (~( 237.26/35.03 in(Y2, 237.26/35.03 Y0)))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!((^[Y2 : $i]: 237.26/35.03 (( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y0))) => 237.26/35.03 (~( 237.26/35.03 in(Y2, 237.26/35.03 setminus( 237.26/35.03 Y0, Y1)))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 Y1) => 237.26/35.03 ( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 setminus( 237.26/35.03 Y0, Y1)))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 subset( 237.26/35.03 setminus( 237.26/35.03 Y0, Y1), 237.26/35.03 Y0))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 ((setminus( 237.26/35.03 Y0, Y1) = 237.26/35.03 emptyset) => 237.26/35.03 subset( 237.26/35.03 Y0, Y1)))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 symdiff( 237.26/35.03 Y0, Y1)) => 237.26/35.03 (!!(( 237.26/35.03 ^[Y3 : $o]: 237.26/35.03 (( 237.26/35.03 in(Y2, 237.26/35.03 Y0) => 237.26/35.03 ( 237.26/35.03 ( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y1))) => 237.26/35.03 Y3)) => 237.26/35.03 (( 237.26/35.03 ( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y0))) => 237.26/35.03 ( 237.26/35.03 in(Y2, 237.26/35.03 Y1) => Y3)) => 237.26/35.03 Y3))))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 ( 237.26/35.03 !!(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 Y0) => 237.26/35.03 (( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y1))) => 237.26/35.03 in(Y2, 237.26/35.03 symdiff( 237.26/35.03 Y0, Y1))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y0))) => 237.26/35.03 (in(Y2, 237.26/35.03 Y1) => 237.26/35.03 in(Y2, 237.26/35.03 symdiff( 237.26/35.03 Y0, Y1))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!((^[Y1 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 Y0) => 237.26/35.03 (in(Y2, 237.26/35.03 Y1) => 237.26/35.03 (~( 237.26/35.03 in(Y2, 237.26/35.03 symdiff( 237.26/35.03 Y0, Y1))))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y0))) => 237.26/35.03 (( 237.26/35.03 ~( 237.26/35.03 in(Y2, 237.26/35.03 Y1))) => 237.26/35.03 (~( 237.26/35.03 in(Y2, 237.26/35.03 symdiff( 237.26/35.03 Y0, Y1))))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 in(Y1, 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 in(Y0, 237.26/35.03 setunion( 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 in(Y1, 237.26/35.03 setunion( 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 ( 237.26/35.03 !!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 (??(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 setunion( 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)))) & 237.26/35.03 (??(( 237.26/35.03 ^[Y3 : $i]: 237.26/35.03 (in(Y3, 237.26/35.03 setunion( 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)))) & 237.26/35.03 (setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)) = 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y2, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y2, 237.26/35.03 setadjoin( 237.26/35.03 Y3, 237.26/35.03 emptyset)), 237.26/35.03 emptyset))))))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 (??(( 237.26/35.03 ^[Y2 : $i]: 237.26/35.03 (in(Y2, 237.26/35.03 setunion( 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)))) & 237.26/35.03 (??(( 237.26/35.03 ^[Y3 : $i]: 237.26/35.03 (in(Y3, 237.26/35.03 setunion( 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)))) & 237.26/35.03 (setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y0, 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset)), 237.26/35.03 emptyset)) = 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y2, 237.26/35.03 emptyset), 237.26/35.03 setadjoin( 237.26/35.03 setadjoin( 237.26/35.03 Y2, 237.26/35.03 setadjoin( 237.26/35.03 Y3, 237.26/35.03 emptyset)), 237.26/35.03 emptyset))))))))))))))))) => 237.26/35.03 ((!!((^[Y0 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 (in(Y1, 237.26/35.03 Y0) => 237.26/35.03 subset( 237.26/35.03 setadjoin( 237.26/35.03 Y1, 237.26/35.03 emptyset), 237.26/35.03 Y0)))))))) => 237.26/35.03 ((!!(( 237.26/35.03 ^[Y0 : $i]: 237.26/35.03 (!!(( 237.26/35.03 ^[Y1 : $i]: 237.26/35.03 (in(Y1, 237.26/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 Y0))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))) => 237.74/35.03 (( 237.74/35.03 Y2 = Y1) | 237.74/35.03 (Y2 = Y0)))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 Y1) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 setunion( 237.74/35.03 Y0)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 in(Y1, 237.74/35.03 Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)), 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)) = 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y2 = Y3))))))))))) => 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y3 = Y2)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.03 inference('lazy_cnf_imply', [status(thm)], ['247'])). 237.74/35.03 tff('249', plain, 237.74/35.03 ~ ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 ((~(in(Y2, Y1))) => (~(subset(Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y2) => 237.74/35.03 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin(Y0, 237.74/35.03 setadjoin(Y1, emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (!!((^[Y3 : $o]: 237.74/35.03 (in(Y2, 237.74/35.03 binunion(Y0, Y1)) => 237.74/35.03 ((in(Y2, Y0) => Y3) => 237.74/35.03 ((in(Y2, Y1) => Y3) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y2, Y0) => 237.74/35.03 (subset(Y2, Y1) => 237.74/35.03 subset(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), 237.74/35.03 Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y1) => 237.74/35.03 subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, 237.74/35.03 Y1)) => 237.74/35.03 in(Y2, Y1))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((~((??((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) & 237.74/35.03 in(Y2, Y1))))))) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 binintersect(Y0, Y1), 237.74/35.03 Y1))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = 237.74/35.03 Y0) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (binintersect( 237.74/35.03 Y0, 237.74/35.03 binunion( 237.74/35.03 Y1, Y2)) = 237.74/35.03 binunion( 237.74/35.03 binintersect( 237.74/35.03 Y0, Y1), 237.74/35.03 binintersect( 237.74/35.03 Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 ((~(in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (~( 237.74/35.03 in(Y2, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (setminus(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in(Y2, 237.74/35.03 Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 setminus( 237.74/35.03 Y0, Y1), 237.74/35.03 Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((setminus( 237.74/35.03 Y0, Y1) = 237.74/35.03 emptyset) => 237.74/35.03 subset(Y0, 237.74/35.03 Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $o]: 237.74/35.03 (( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 Y3)) => 237.74/35.03 (( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => Y3)) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 in(Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 Y0))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))) => 237.74/35.03 (( 237.74/35.03 Y2 = Y1) | 237.74/35.03 (Y2 = Y0)))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 Y1) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 setunion( 237.74/35.03 Y0)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 in(Y1, 237.74/35.03 Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)), 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)) = 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y2 = Y3))))))))))) => 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y3 = Y2)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.03 inference('lazy_cnf_imply', [status(thm)], ['248'])). 237.74/35.03 tff('250', plain, 237.74/35.03 ~ ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: ((~(subset(Y0, Y1))) => (Y0 != Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y2) => 237.74/35.03 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (!!((^[Y3 : $o]: 237.74/35.03 (in(Y2, 237.74/35.03 binunion(Y0, Y1)) => 237.74/35.03 ((in(Y2, Y0) => Y3) => 237.74/35.03 ((in(Y2, Y1) => Y3) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y2, Y0) => 237.74/35.03 (subset(Y2, Y1) => 237.74/35.03 subset(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), 237.74/35.03 Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y1) => 237.74/35.03 subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, 237.74/35.03 Y1)) => 237.74/35.03 in(Y2, Y1))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((~((??((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) & 237.74/35.03 in(Y2, Y1))))))) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 binintersect(Y0, Y1), 237.74/35.03 Y1))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = 237.74/35.03 Y0) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (binintersect( 237.74/35.03 Y0, 237.74/35.03 binunion(Y1, 237.74/35.03 Y2)) = 237.74/35.03 binunion( 237.74/35.03 binintersect( 237.74/35.03 Y0, Y1), 237.74/35.03 binintersect( 237.74/35.03 Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 ((~(in(Y2, Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (~(in(Y2, 237.74/35.03 Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (setminus(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in(Y2, 237.74/35.03 Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 setminus( 237.74/35.03 Y0, Y1), 237.74/35.03 Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((setminus( 237.74/35.03 Y0, Y1) = 237.74/35.03 emptyset) => 237.74/35.03 subset(Y0, 237.74/35.03 Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1)) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $o]: 237.74/35.03 (( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 Y3)) => 237.74/35.03 (( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => Y3)) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 in(Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))) => 237.74/35.03 (( 237.74/35.03 Y2 = Y1) | 237.74/35.03 (Y2 = Y0)))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 Y1) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 setunion( 237.74/35.03 Y0)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 in(Y1, 237.74/35.03 Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)), 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)) = 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y2 = Y3))))))))))) => 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y3 = Y2)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.03 inference('lazy_cnf_imply', [status(thm)], ['249'])). 237.74/35.03 tff('251', plain, 237.74/35.03 ~ ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => ((~(in(Y2, Y1))) => (Y0 != Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y2) => 237.74/35.03 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (!!((^[Y3 : $o]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 ((in(Y2, Y0) => Y3) => 237.74/35.03 ((in(Y2, Y1) => Y3) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y2, Y0) => 237.74/35.03 (subset(Y2, Y1) => 237.74/35.03 subset(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y1) => 237.74/35.03 subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, 237.74/35.03 Y1)) => 237.74/35.03 in(Y2, Y1))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((~((??((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) & 237.74/35.03 in(Y2, Y1))))))) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 binintersect(Y0, Y1), Y1))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = 237.74/35.03 Y0) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (binintersect( 237.74/35.03 Y0, 237.74/35.03 binunion(Y1, 237.74/35.03 Y2)) = 237.74/35.03 binunion( 237.74/35.03 binintersect( 237.74/35.03 Y0, Y1), 237.74/35.03 binintersect( 237.74/35.03 Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 ((~(in(Y2, Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (~(in(Y2, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (setminus(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 setminus(Y0, 237.74/35.03 Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((setminus( 237.74/35.03 Y0, Y1) = 237.74/35.03 emptyset) => 237.74/35.03 subset(Y0, 237.74/35.03 Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1)) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $o]: 237.74/35.03 (( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 Y3)) => 237.74/35.03 (( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => Y3)) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 ( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))) => 237.74/35.03 (( 237.74/35.03 Y2 = Y1) | 237.74/35.03 (Y2 = Y0)))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 Y1) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 setunion( 237.74/35.03 Y0)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 in(Y1, 237.74/35.03 Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)), 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)) = 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y2 = Y3))))))))))) => 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y3 = Y2)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.03 inference('lazy_cnf_imply', [status(thm)], ['250'])). 237.74/35.03 tff('252', plain, 237.74/35.03 ~ ((!!((^[Y0 : $i]: subset(Y0, Y0)))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y2) => 237.74/35.03 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (!!((^[Y3 : $o]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 ((in(Y2, Y0) => Y3) => 237.74/35.03 ((in(Y2, Y1) => Y3) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y2, Y0) => 237.74/35.03 (subset(Y2, Y1) => 237.74/35.03 subset(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y1) => 237.74/35.03 subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y1))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((~((??((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) & 237.74/35.03 in(Y2, Y1))))))) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 binintersect(Y0, Y1), Y1))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => 237.74/35.03 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = 237.74/35.03 Y0) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (binintersect(Y0, 237.74/35.03 binunion(Y1, 237.74/35.03 Y2)) = 237.74/35.03 binunion( 237.74/35.03 binintersect( 237.74/35.03 Y0, Y1), 237.74/35.03 binintersect( 237.74/35.03 Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 ((~(in(Y2, Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (~(in(Y2, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (setminus(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~(in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 ((~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 Y0)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 setminus(Y0, 237.74/35.03 Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((setminus(Y0, 237.74/35.03 Y1) = 237.74/35.03 emptyset) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $o]: 237.74/35.03 (( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 Y3)) => 237.74/35.03 (( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => Y3)) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (in(Y2, 237.74/35.03 Y1) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 ( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))) => 237.74/35.03 (( 237.74/35.03 Y2 = Y1) | 237.74/35.03 (Y2 = Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 Y1) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 setunion( 237.74/35.03 Y0)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 in(Y1, 237.74/35.03 Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)), 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)) = 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y2 = Y3))))))))))) => 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y3 = Y2)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.03 inference('lazy_cnf_imply', [status(thm)], ['251'])). 237.74/35.03 tff('253', plain, 237.74/35.03 ~ ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (subset(Y1, Y2) => subset(Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y2) => 237.74/35.03 subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (!!((^[Y3 : $o]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 ((in(Y2, Y0) => Y3) => 237.74/35.03 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y2, Y0) => 237.74/35.03 (subset(Y2, Y1) => 237.74/35.03 subset(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y1) => 237.74/35.03 subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y1))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((~((??((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) & 237.74/35.03 in(Y2, Y1))))))) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), 237.74/35.03 Y1))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => 237.74/35.03 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y0) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (binintersect(Y0, 237.74/35.03 binunion(Y1, Y2)) = 237.74/35.03 binunion( 237.74/35.03 binintersect( 237.74/35.03 Y0, Y1), 237.74/35.03 binintersect( 237.74/35.03 Y0, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 ((~(in(Y2, Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1)) => 237.74/35.03 (~(in(Y2, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (setminus(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~(in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~(in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 ((~( 237.74/35.03 in(Y2, Y1))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, Y0)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~( 237.74/35.03 in(Y2, Y0))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset( 237.74/35.03 setminus(Y0, 237.74/35.03 Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((setminus(Y0, 237.74/35.03 Y1) = 237.74/35.03 emptyset) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $o]: 237.74/35.03 (( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 Y3)) => 237.74/35.03 (( 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => Y3)) => 237.74/35.03 Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y0) => 237.74/35.03 ( 237.74/35.03 in(Y2, 237.74/35.03 Y1) => 237.74/35.03 ( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (( 237.74/35.03 ~( 237.74/35.03 in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 (~( 237.74/35.03 in(Y2, 237.74/35.03 symdiff( 237.74/35.03 Y0, Y1))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)))) & 237.74/35.03 (setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)) = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 ( 237.74/35.03 in(Y1, 237.74/35.03 Y0) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 setadjoin( 237.74/35.03 Y1, 237.74/35.03 emptyset))) => 237.74/35.03 (( 237.74/35.03 Y2 = Y1) | 237.74/35.03 (Y2 = Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 subset( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 powerset( 237.74/35.03 powerset( 237.74/35.03 binunion( 237.74/35.03 Y0, Y1)))))))))))))))))) => 237.74/35.03 ((!!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y1) => 237.74/35.03 in( 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset)), 237.74/35.03 emptyset)), 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)))))))))))))))) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 Y1) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 cartprod( 237.74/35.03 Y0, Y1)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (??(( 237.74/35.03 ^[Y4 : $i]: 237.74/35.03 (in(Y4, 237.74/35.03 setunion( 237.74/35.03 Y2)) & 237.74/35.03 (Y2 = 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset), 237.74/35.03 setadjoin( 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 setadjoin( 237.74/35.03 Y4, 237.74/35.03 emptyset)), 237.74/35.03 emptyset))))))))))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i]: 237.74/35.03 (in(Y1, 237.74/35.03 setunion( 237.74/35.03 Y0)) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 in(Y1, 237.74/35.03 Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)), 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 subset( 237.74/35.03 Y0, 237.74/35.03 setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (setunion( 237.74/35.03 setadjoin( 237.74/35.03 Y0, 237.74/35.03 emptyset)) = 237.74/35.03 Y0)))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (!!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y2 = Y3))))))))))) => 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))))))))))) => 237.74/35.03 ( 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (( 237.74/35.03 ??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y2, 237.74/35.03 emptyset)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) & 237.74/35.03 Y1(Y2)))))))))))) => 237.74/35.03 ( 237.74/35.03 !!(( 237.74/35.03 ^[Y0 : $i]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y1 : $i > $o]: 237.74/35.03 (!!(( 237.74/35.03 ^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y2) => 237.74/35.03 (( 237.74/35.03 !!(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 Y0) => 237.74/35.03 (Y1(Y3) => 237.74/35.03 (Y3 = Y2)))))) => 237.74/35.03 (??(( 237.74/35.03 ^[Y3 : $i]: 237.74/35.03 (in(Y3, 237.74/35.03 dsetconstr( 237.74/35.03 Y0, Y1)) & 237.74/35.03 (dsetconstr( 237.74/35.03 Y0, Y1) = 237.74/35.03 setadjoin( 237.74/35.03 Y3, 237.74/35.03 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.03 inference('lazy_cnf_imply', [status(thm)], ['252'])). 237.74/35.03 tff('254', plain, 237.74/35.03 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, setadjoin(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y0, Y2) => subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: 237.74/35.03 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 in(Y1, 237.74/35.03 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (!!((^[Y3 : $o]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 ((in(Y2, Y0) => Y3) => 237.74/35.03 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, binunion(Y0, Y1)) => 237.74/35.03 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 (in(Y2, Y1) => 237.74/35.03 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (subset(Y2, Y0) => 237.74/35.03 (subset(Y2, Y1) => 237.74/35.03 subset(Y2, 237.74/35.03 binintersect(Y0, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y1) => 237.74/35.03 subset(Y1, Y0)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 binintersect(Y0, Y1)) => 237.74/35.03 in(Y2, Y1))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((~((??((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) & 237.74/35.03 in(Y2, Y1))))))) => 237.74/35.03 (binintersect(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 subset(binintersect(Y0, Y1), 237.74/35.03 Y1))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y1, Y0) => 237.74/35.03 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 ((binintersect(Y0, Y1) = Y0) => 237.74/35.03 subset(Y0, Y1)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (binintersect(Y0, 237.74/35.03 binunion(Y1, Y2)) = 237.74/35.03 binunion( 237.74/35.03 binintersect(Y0, 237.74/35.03 Y1), 237.74/35.03 binintersect(Y0, 237.74/35.03 Y2)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 ((~(in(Y2, Y1))) => 237.74/35.03 in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1)) => 237.74/35.03 in(Y2, Y0))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 (in(Y2, 237.74/35.03 setminus(Y0, 237.74/35.03 Y1)) => 237.74/35.03 (~(in(Y2, Y1))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (subset(Y0, Y1) => 237.74/35.03 (setminus(Y0, Y1) = 237.74/35.03 emptyset)))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~(in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 (in(Y2, Y0) => 237.74/35.03 in(Y2, Y1)))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~(in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))) => 237.74/35.03 ((~(in(Y2, 237.74/35.03 Y1))) => 237.74/35.03 (~(in(Y2, 237.74/35.03 Y0)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.03 (!!((^[Y1 : $i]: 237.74/35.03 (!!((^[Y2 : $i]: 237.74/35.03 ((~(in(Y2, 237.74/35.03 Y0))) => 237.74/35.03 (~(in(Y2, 237.74/35.03 setminus( 237.74/35.03 Y0, Y1)))))))))))))) => 237.74/35.03 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~( 237.74/35.04 in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset( 237.74/35.04 setminus(Y0, Y1), 237.74/35.04 Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((setminus(Y0, 237.74/35.04 Y1) = 237.74/35.04 emptyset) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1)) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $o]: 237.74/35.04 (( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 Y3)) => 237.74/35.04 (( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => Y3)) => 237.74/35.04 Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 (in(Y2, 237.74/35.04 Y1) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y1, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))) => 237.74/35.04 (( 237.74/35.04 Y2 = Y1) | 237.74/35.04 (Y2 = Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 Y1) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 setunion( 237.74/35.04 Y0)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 in(Y1, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)), 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)) = 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y2 = Y3))))))))))) => 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y3 = Y2)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.04 inference('lazy_cnf_imply', [status(thm)], ['253'])). 237.74/35.04 tff('255', plain, 237.74/35.04 ~ ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y0, Y2) => subset(Y0, setadjoin(Y1, Y2)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: 237.74/35.04 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 ((in(Y2, Y0) => Y3) => 237.74/35.04 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y2, Y0) => 237.74/35.04 (subset(Y2, Y1) => 237.74/35.04 subset(Y2, 237.74/35.04 binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y1) => 237.74/35.04 subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y1))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((~((??((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) & 237.74/35.04 in(Y2, Y1))))))) => 237.74/35.04 (binintersect(Y0, Y1) = 237.74/35.04 emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), 237.74/35.04 Y1))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y1, Y0) => 237.74/35.04 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y0) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (binintersect(Y0, 237.74/35.04 binunion(Y1, Y2)) = 237.74/35.04 binunion( 237.74/35.04 binintersect(Y0, 237.74/35.04 Y1), 237.74/35.04 binintersect(Y0, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 setminus(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, 237.74/35.04 Y1)) => 237.74/35.04 (~(in(Y2, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (setminus(Y0, Y1) = 237.74/35.04 emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))) => 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 in(Y2, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 (~(in(Y2, Y0)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, Y0))) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset( 237.74/35.04 setminus(Y0, Y1), 237.74/35.04 Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((setminus(Y0, Y1) = 237.74/35.04 emptyset) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1)) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $o]: 237.74/35.04 (( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 Y3)) => 237.74/35.04 (( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => Y3)) => 237.74/35.04 Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 (in(Y2, 237.74/35.04 Y1) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (in(Y2, 237.74/35.04 Y1) => 237.74/35.04 (~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))) => 237.74/35.04 (( 237.74/35.04 Y2 = Y1) | 237.74/35.04 (Y2 = Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 Y1) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 setunion( 237.74/35.04 Y0)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 in(Y1, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)), 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)) = 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y2 = Y3))))))))))) => 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y3 = Y2)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.04 inference('lazy_cnf_imply', [status(thm)], ['254'])). 237.74/35.04 tff('256', plain, 237.74/35.04 ~ ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (subset(Y0, Y1) => in(Y0, powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: 237.74/35.04 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 ((in(Y2, Y0) => Y3) => 237.74/35.04 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y2, Y0) => 237.74/35.04 (subset(Y2, Y1) => 237.74/35.04 subset(Y2, 237.74/35.04 binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y1) => 237.74/35.04 subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y1))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((~((??((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) & 237.74/35.04 in(Y2, Y1))))))) => 237.74/35.04 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y1, Y0) => 237.74/35.04 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y0) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (binintersect(Y0, 237.74/35.04 binunion(Y1, Y2)) = 237.74/35.04 binunion( 237.74/35.04 binintersect(Y0, 237.74/35.04 Y1), 237.74/35.04 binintersect(Y0, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 setminus(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 (~(in(Y2, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (setminus(Y0, Y1) = 237.74/35.04 emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))) => 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 in(Y2, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 (~(in(Y2, Y0)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, Y0))) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset( 237.74/35.04 setminus(Y0, Y1), 237.74/35.04 Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((setminus(Y0, Y1) = 237.74/35.04 emptyset) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $o]: 237.74/35.04 (( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 Y3)) => 237.74/35.04 (( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => Y3)) => 237.74/35.04 Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (in(Y2, 237.74/35.04 Y1) => 237.74/35.04 (~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 (~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))) => 237.74/35.04 (( 237.74/35.04 Y2 = Y1) | 237.74/35.04 (Y2 = Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 Y1) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 setunion( 237.74/35.04 Y0)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 in(Y1, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)), 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)) = 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y2 = Y3))))))))))) => 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y3 = Y2)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.04 inference('lazy_cnf_imply', [status(thm)], ['255'])). 237.74/35.04 tff('257', plain, 237.74/35.04 ~ ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => (subset(Y1, Y0) => (Y0 = Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: 237.74/35.04 in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 ((in(Y2, Y0) => Y3) => 237.74/35.04 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y2, Y0) => 237.74/35.04 (subset(Y2, Y1) => 237.74/35.04 subset(Y2, 237.74/35.04 binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y1) => 237.74/35.04 subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y1))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((~((??((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) & 237.74/35.04 in(Y2, Y1))))))) => 237.74/35.04 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y1, Y0) => 237.74/35.04 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y0) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (binintersect(Y0, 237.74/35.04 binunion(Y1, Y2)) = 237.74/35.04 binunion( 237.74/35.04 binintersect(Y0, Y1), 237.74/35.04 binintersect(Y0, Y2)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 setminus(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 (~(in(Y2, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (setminus(Y0, Y1) = 237.74/35.04 emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))) => 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 in(Y2, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 (~(in(Y2, Y0)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, Y0))) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset( 237.74/35.04 setminus(Y0, Y1), 237.74/35.04 Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((setminus(Y0, Y1) = 237.74/35.04 emptyset) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $o]: 237.74/35.04 (( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 Y3)) => 237.74/35.04 (( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => Y3)) => 237.74/35.04 Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 (~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y1, 237.74/35.04 Y0) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))) => 237.74/35.04 (( 237.74/35.04 Y2 = Y1) | 237.74/35.04 (Y2 = Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 Y1) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 setunion( 237.74/35.04 Y0)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 in(Y1, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)), 237.74/35.04 Y0)))) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)) = 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y2 = Y3))))))))))) => 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y3 = Y2)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.04 inference('lazy_cnf_imply', [status(thm)], ['256'])). 237.74/35.04 tff('258', plain, 237.74/35.04 ~ ((!!((^[Y0 : $i]: (subset(Y0, emptyset) => (Y0 = emptyset))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 ((in(Y2, Y0) => Y3) => 237.74/35.04 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y2, Y0) => 237.74/35.04 (subset(Y2, Y1) => 237.74/35.04 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y1) => 237.74/35.04 subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y1))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((~((??((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.04 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y1, Y0) => 237.74/35.04 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y0) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (binintersect(Y0, 237.74/35.04 binunion(Y1, Y2)) = 237.74/35.04 binunion( 237.74/35.04 binintersect(Y0, Y1), 237.74/35.04 binintersect(Y0, Y2)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 setminus(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 (~(in(Y2, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (setminus(Y0, Y1) = 237.74/35.04 emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus(Y0, 237.74/35.04 Y1)))) => 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 in(Y2, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 (~(in(Y2, Y0)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, Y0))) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset( 237.74/35.04 setminus(Y0, Y1), 237.74/35.04 Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((setminus(Y0, Y1) = 237.74/35.04 emptyset) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $o]: 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 Y3)) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => Y3)) => 237.74/35.04 Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 (in(Y2, 237.74/35.04 Y1) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 ( 237.74/35.04 ??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y1, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))) => 237.74/35.04 (( 237.74/35.04 Y2 = Y1) | 237.74/35.04 (Y2 = Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 Y1) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 setunion( 237.74/35.04 Y0)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 in(Y1, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)), 237.74/35.04 Y0)))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)))))) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)) = 237.74/35.04 Y0)))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y2 = Y3))))))))))) => 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y3 = Y2)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.04 inference('lazy_cnf_imply', [status(thm)], ['257'])). 237.74/35.04 tff('259', plain, 237.74/35.04 ~ ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (subset(Y1, Y0) => in(Y1, powerset(Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 ((in(Y2, Y0) => Y3) => 237.74/35.04 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y2, Y0) => 237.74/35.04 (subset(Y2, Y1) => 237.74/35.04 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y1) => 237.74/35.04 subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y1))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((~((??((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.04 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y1, Y0) => 237.74/35.04 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y0) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (binintersect(Y0, 237.74/35.04 binunion(Y1, Y2)) = 237.74/35.04 binunion( 237.74/35.04 binintersect(Y0, Y1), 237.74/35.04 binintersect(Y0, Y2)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 setminus(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 (~(in(Y2, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (setminus(Y0, Y1) = 237.74/35.04 emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus(Y0, 237.74/35.04 Y1)))) => 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 in(Y2, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus(Y0, 237.74/35.04 Y1)))) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 (~(in(Y2, Y0)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, Y0))) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset( 237.74/35.04 setminus(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((setminus(Y0, Y1) = 237.74/35.04 emptyset) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $o]: 237.74/35.04 (( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 Y3)) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => Y3)) => 237.74/35.04 Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~( 237.74/35.04 in(Y2, Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~( 237.74/35.04 in(Y2, Y0))) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, 237.74/35.04 Y1) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin(Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 ( 237.74/35.04 ??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 ( 237.74/35.04 ??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, Y0) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))) => 237.74/35.04 (( 237.74/35.04 Y2 = Y1) | 237.74/35.04 (Y2 = Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 Y1) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 setunion( 237.74/35.04 Y0)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 in(Y1, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)), 237.74/35.04 Y0)))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)) = 237.74/35.04 Y0)))) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y2 = Y3))))))))))) => 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))))))))))) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y3 = Y2)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.04 inference('lazy_cnf_imply', [status(thm)], ['258'])). 237.74/35.04 tff('260', plain, 237.74/35.04 ~ ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: (in(Y1, powerset(Y0)) => subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 ((in(Y2, Y0) => Y3) => 237.74/35.04 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y2, Y0) => 237.74/35.04 (subset(Y2, Y1) => 237.74/35.04 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y1) => 237.74/35.04 subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y1))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((~((??((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.04 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y1, Y0) => 237.74/35.04 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y0) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (binintersect(Y0, 237.74/35.04 binunion(Y1, Y2)) = 237.74/35.04 binunion( 237.74/35.04 binintersect(Y0, Y1), 237.74/35.04 binintersect(Y0, Y2)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 setminus(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setminus(Y0, Y1)) => 237.74/35.04 (~(in(Y2, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus(Y0, 237.74/35.04 Y1)))) => 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 in(Y2, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 setminus(Y0, 237.74/35.04 Y1)))) => 237.74/35.04 ((~(in(Y2, Y1))) => 237.74/35.04 (~(in(Y2, Y0)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, Y0))) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus(Y0, 237.74/35.04 Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~(in(Y2, 237.74/35.04 setminus( 237.74/35.04 Y0, Y1)))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 subset( 237.74/35.04 setminus(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((setminus(Y0, Y1) = 237.74/35.04 emptyset) => 237.74/35.04 subset(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 symdiff(Y0, 237.74/35.04 Y1)) => 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (( 237.74/35.04 in(Y2, 237.74/35.04 Y0) => 237.74/35.04 ( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 Y3)) => 237.74/35.04 (( 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 ( 237.74/35.04 in(Y2, 237.74/35.04 Y1) => Y3)) => 237.74/35.04 Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 ((~(in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~(in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 (~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 ((~( 237.74/35.04 in(Y2, 237.74/35.04 Y0))) => 237.74/35.04 (( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 Y1))) => 237.74/35.04 ( 237.74/35.04 ~( 237.74/35.04 in(Y2, 237.74/35.04 symdiff( 237.74/35.04 Y0, Y1))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setadjoin(Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??((^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 ( 237.74/35.04 ??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)))) & 237.74/35.04 (setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)) = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, Y0) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (in(Y1, Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 Y0))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 setadjoin( 237.74/35.04 Y1, 237.74/35.04 emptyset))) => 237.74/35.04 (( 237.74/35.04 Y2 = Y1) | 237.74/35.04 (Y2 = Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 subset( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 powerset( 237.74/35.04 powerset( 237.74/35.04 binunion( 237.74/35.04 Y0, Y1)))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y1) => 237.74/35.04 in( 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)), 237.74/35.04 emptyset)), 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 Y1) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 cartprod( 237.74/35.04 Y0, Y1)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (??(( 237.74/35.04 ^[Y4 : $i]: 237.74/35.04 (in(Y4, 237.74/35.04 setunion( 237.74/35.04 Y2)) & 237.74/35.04 (Y2 = 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset), 237.74/35.04 setadjoin( 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 setadjoin( 237.74/35.04 Y4, 237.74/35.04 emptyset)), 237.74/35.04 emptyset))))))))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i]: 237.74/35.04 (in(Y1, 237.74/35.04 setunion( 237.74/35.04 Y0)) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 in(Y1, 237.74/35.04 Y2)))))))))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)), 237.74/35.04 Y0)))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 subset( 237.74/35.04 Y0, 237.74/35.04 setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)))))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (setunion( 237.74/35.04 setadjoin( 237.74/35.04 Y0, 237.74/35.04 emptyset)) = 237.74/35.04 Y0)))) => 237.74/35.04 ((!!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (!!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y2 = Y3))))))))))) => 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))))))))))) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (( 237.74/35.04 ??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y2, 237.74/35.04 emptyset)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) & 237.74/35.04 Y1(Y2)))))))))))) => 237.74/35.04 ( 237.74/35.04 !!(( 237.74/35.04 ^[Y0 : $i]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y1 : $i > $o]: 237.74/35.04 (!!(( 237.74/35.04 ^[Y2 : $i]: 237.74/35.04 (in(Y2, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y2) => 237.74/35.04 (( 237.74/35.04 !!(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 Y0) => 237.74/35.04 (Y1(Y3) => 237.74/35.04 (Y3 = Y2)))))) => 237.74/35.04 (??(( 237.74/35.04 ^[Y3 : $i]: 237.74/35.04 (in(Y3, 237.74/35.04 dsetconstr( 237.74/35.04 Y0, Y1)) & 237.74/35.04 (dsetconstr( 237.74/35.04 Y0, Y1) = 237.74/35.04 setadjoin( 237.74/35.04 Y3, 237.74/35.04 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.04 inference('lazy_cnf_imply', [status(thm)], ['259'])). 237.74/35.04 tff('261', plain, 237.74/35.04 ~ ((!!((^[Y0 : $i]: in(Y0, powerset(Y0))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (!!((^[Y3 : $o]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 ((in(Y2, Y0) => Y3) => 237.74/35.04 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binunion(Y0, Y1)) => 237.74/35.04 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, Y0) => 237.74/35.04 (in(Y2, Y1) => 237.74/35.04 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (subset(Y2, Y0) => 237.74/35.04 (subset(Y2, Y1) => 237.74/35.04 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y0))))))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (subset(Y0, Y1) => 237.74/35.04 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 ((binintersect(Y0, Y1) = Y1) => 237.74/35.04 subset(Y1, Y0)))))))) => 237.74/35.04 ((!!((^[Y0 : $i]: 237.74/35.04 (!!((^[Y1 : $i]: 237.74/35.04 (!!((^[Y2 : $i]: 237.74/35.04 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.04 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion( 237.74/35.05 binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, 237.74/35.05 Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, 237.74/35.05 Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, 237.74/35.05 Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), 237.74/35.05 Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = 237.74/35.05 emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 (( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y1) => Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~( 237.74/35.05 in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~( 237.74/35.05 in(Y2, Y0))) => 237.74/35.05 ((~( 237.74/35.05 in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 (~( 237.74/35.05 in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 (( 237.74/35.05 Y2 = Y1) | 237.74/35.05 (Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)) = 237.74/35.05 Y0)))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y2 = Y3))))))))))) => 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))))))))))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2)))))))))))) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y3 = Y2)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.05 inference('lazy_cnf_imply', [status(thm)], ['260'])). 237.74/35.05 tff('262', plain, 237.74/35.05 ~ ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => subset(powerset(Y0), powerset(Y1))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 ((in(Y2, Y0) => Y3) => 237.74/35.05 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (subset(Y2, Y0) => 237.74/35.05 (subset(Y2, Y1) => 237.74/35.05 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y1) => 237.74/35.05 subset(Y1, Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion( 237.74/35.05 binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, 237.74/35.05 Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, 237.74/35.05 Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), 237.74/35.05 Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = 237.74/35.05 emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y1) => Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 ((~( 237.74/35.05 in(Y2, Y1))) => 237.74/35.05 (~( 237.74/35.05 in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 ??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 (( 237.74/35.05 Y2 = Y1) | 237.74/35.05 (Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)) = 237.74/35.05 Y0)))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y2 = Y3))))))))))) => 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))))))))))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2)))))))))))) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y3 = Y2)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.05 inference('lazy_cnf_imply', [status(thm)], ['261'])). 237.74/35.05 tff('263', plain, 237.74/35.05 ~ ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i > $o]: in(dsetconstr(Y0, Y1), powerset(Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 ((in(Y2, Y0) => Y3) => 237.74/35.05 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (subset(Y2, Y0) => 237.74/35.05 (subset(Y2, Y1) => 237.74/35.05 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y1) => 237.74/35.05 subset(Y1, Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion( 237.74/35.05 binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, 237.74/35.05 Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), 237.74/35.05 Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = 237.74/35.05 emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y1) => Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 ((~(in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 ??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 ??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 Y2 = Y1) | 237.74/35.05 ( 237.74/35.05 Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)) = 237.74/35.05 Y0)))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y2 = Y3))))))))))) => 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))))))))))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2)))))))))))) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y3 = Y2)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.05 inference('lazy_cnf_imply', [status(thm)], ['262'])). 237.74/35.05 tff('264', plain, 237.74/35.05 ~ ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i > $o]: subset(dsetconstr(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 ((in(Y2, Y0) => Y3) => 237.74/35.05 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (subset(Y2, Y0) => 237.74/35.05 (subset(Y2, Y1) => 237.74/35.05 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y1) => 237.74/35.05 subset(Y1, Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion( 237.74/35.05 binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = 237.74/35.05 emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 ((in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 (( 237.74/35.05 ( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y1) => Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 ??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset(Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 Y2 = Y1) | 237.74/35.05 ( 237.74/35.05 Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)) = 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y2 = Y3))))))))))) => 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))))))))))) => 237.74/35.05 ((!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2)))))))))))) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y3 = Y2)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.05 inference('lazy_cnf_imply', [status(thm)], ['263'])). 237.74/35.05 tff('265', plain, 237.74/35.05 ~ ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 ((in(Y2, Y0) => Y3) => 237.74/35.05 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (subset(Y2, Y0) => 237.74/35.05 (subset(Y2, Y1) => 237.74/35.05 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y1) => 237.74/35.05 subset(Y1, Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion( 237.74/35.05 binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = 237.74/35.05 emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 ((in(Y2, Y0) => 237.74/35.05 (( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 ((( 237.74/35.05 ~( 237.74/35.05 in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y1) => Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset), 237.74/35.05 Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset(Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 (( 237.74/35.05 Y2 = Y1) | 237.74/35.05 (Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 ( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)) = 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y2 = Y3))))))))))) => 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2)))))))))))) => 237.74/35.05 (!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y3 = Y2)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.05 inference('lazy_cnf_imply', [status(thm)], ['264'])). 237.74/35.05 tff('266', plain, 237.74/35.05 ~ ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 ((in(Y2, Y0) => Y3) => 237.74/35.05 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (subset(Y2, Y0) => 237.74/35.05 (subset(Y2, Y1) => 237.74/35.05 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y1) => 237.74/35.05 subset(Y1, Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion(binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 ((in(Y2, Y0) => 237.74/35.05 ((~( 237.74/35.05 in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 (((~( 237.74/35.05 in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 (in(Y2, 237.74/35.05 Y1) => Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset), 237.74/35.05 Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset(Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 (( 237.74/35.05 Y2 = Y1) | 237.74/35.05 (Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i]: 237.74/35.05 (in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 ( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)) = 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y2 = Y3))))))))))) => 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2)))))))))))) => 237.74/35.05 (!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y3 = Y2)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.05 inference('lazy_cnf_imply', [status(thm)], ['265'])). 237.74/35.05 tff('267', plain, 237.74/35.05 ~ ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => in(Y2, binunion(Y0, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 ((in(Y2, Y0) => Y3) => 237.74/35.05 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (subset(Y2, Y0) => 237.74/35.05 (subset(Y2, Y1) => 237.74/35.05 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion(binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 ((in(Y2, Y0) => 237.74/35.05 ((~( 237.74/35.05 in(Y2, Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 (((~( 237.74/35.05 in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff( 237.74/35.05 Y0, Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset), Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset(Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 Y2 = Y1) | 237.74/35.05 ( 237.74/35.05 Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)) = 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y2 = Y3))))))))))) => 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (( 237.74/35.05 ??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 Y1(Y2)))))))))))) => 237.74/35.05 (!!((^[Y0 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y1 : $i > $o]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y2) => 237.74/35.05 (( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) => 237.74/35.05 (Y1(Y3) => 237.74/35.05 (Y3 = Y2)))))) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 dsetconstr( 237.74/35.05 Y0, Y1)) & 237.74/35.05 (dsetconstr( 237.74/35.05 Y0, Y1) = 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.05 inference('lazy_cnf_imply', [status(thm)], ['266'])). 237.74/35.05 tff('268', plain, 237.74/35.05 ~ ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 ((in(Y2, Y0) => Y3) => 237.74/35.05 ((in(Y2, Y1) => Y3) => Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binunion(Y0, Y1)) => 237.74/35.05 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (subset(Y2, Y0) => 237.74/35.05 (subset(Y2, Y1) => 237.74/35.05 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.05 in(Y2, Y1))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((~((??((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.05 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y1, Y0) => 237.74/35.05 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((binintersect(Y0, Y1) = Y0) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (binintersect(Y0, 237.74/35.05 binunion(Y1, Y2)) = 237.74/35.05 binunion(binintersect(Y0, Y1), 237.74/35.05 binintersect(Y0, Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 in(Y2, Y0))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, setminus(Y0, Y1)) => 237.74/35.05 (~(in(Y2, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (subset(Y0, Y1) => 237.74/35.05 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.05 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, Y0)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 setminus(Y0, Y1)))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ((setminus(Y0, Y1) = emptyset) => 237.74/35.05 subset(Y0, Y1)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 symdiff(Y0, Y1)) => 237.74/35.05 (!!((^[Y3 : $o]: 237.74/35.05 ((in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, 237.74/35.05 Y1))) => 237.74/35.05 Y3)) => 237.74/35.05 (((~(in(Y2, 237.74/35.05 Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 Y3)) => 237.74/35.05 Y3))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 in(Y2, 237.74/35.05 symdiff(Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 (in(Y2, Y1) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ((~(in(Y2, Y0))) => 237.74/35.05 ((~(in(Y2, Y1))) => 237.74/35.05 (~(in(Y2, 237.74/35.05 symdiff(Y0, 237.74/35.05 Y1))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 in(Y1, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin(Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??((^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (??((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)))) & 237.74/35.05 ( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)) = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 subset( 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset), Y0)))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin(Y1, 237.74/35.05 emptyset), 237.74/35.05 powerset(Y0))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, Y0) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 setadjoin( 237.74/35.05 Y1, 237.74/35.05 emptyset))) => 237.74/35.05 ( 237.74/35.05 ( 237.74/35.05 Y2 = Y1) | 237.74/35.05 ( 237.74/35.05 Y2 = Y0)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!((^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 subset( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 ( 237.74/35.05 in(Y2, 237.74/35.05 Y0) => 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 powerset( 237.74/35.05 powerset( 237.74/35.05 binunion( 237.74/35.05 Y0, Y1)))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) => 237.74/35.05 (!!(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y1) => 237.74/35.05 in( 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y2, 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset)), 237.74/35.05 emptyset)), 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (!!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 Y0) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 Y1) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 ( 237.74/35.05 !!(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 cartprod( 237.74/35.05 Y0, Y1)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y3 : $i]: 237.74/35.05 (in(Y3, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (??(( 237.74/35.05 ^[Y4 : $i]: 237.74/35.05 (in(Y4, 237.74/35.05 setunion( 237.74/35.05 Y2)) & 237.74/35.05 (Y2 = 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 emptyset), 237.74/35.05 setadjoin( 237.74/35.05 setadjoin( 237.74/35.05 Y3, 237.74/35.05 setadjoin( 237.74/35.05 Y4, 237.74/35.05 emptyset)), 237.74/35.05 emptyset))))))))))))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 (!!((^[Y1 : $i]: 237.74/35.05 (in(Y1, 237.74/35.05 setunion( 237.74/35.05 Y0)) => 237.74/35.05 (??(( 237.74/35.05 ^[Y2 : $i]: 237.74/35.05 (in(Y2, 237.74/35.05 Y0) & 237.74/35.05 in(Y1, 237.74/35.05 Y2)))))))))))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset( 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)), 237.74/35.05 Y0)))) => 237.74/35.05 ((!!((^[Y0 : $i]: 237.74/35.05 subset(Y0, 237.74/35.05 setunion( 237.74/35.05 setadjoin( 237.74/35.05 Y0, 237.74/35.05 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['267'])). 237.74/35.06 tff('269', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binunion(Y0, Y1)) => 237.74/35.06 (in(Y2, Y1) | in(Y2, Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (subset(Y2, Y0) => 237.74/35.06 (subset(Y2, Y1) => 237.74/35.06 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.06 in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => 237.74/35.06 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, 237.74/35.06 Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, 237.74/35.06 Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 (( 237.74/35.06 Y2 = Y1) | 237.74/35.06 ( 237.74/35.06 Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 Y0)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)), 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['268'])). 237.74/35.06 tff('270', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y0, binunion(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (subset(Y2, Y0) => 237.74/35.06 (subset(Y2, Y1) => 237.74/35.06 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.06 in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => 237.74/35.06 (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, 237.74/35.06 Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 ( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion( 237.74/35.06 Y0)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)), 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['269'])). 237.74/35.06 tff('271', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(Y1, binunion(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (subset(Y2, Y0) => 237.74/35.06 (subset(Y2, Y1) => 237.74/35.06 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => 237.74/35.06 in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 ( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 ( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion( 237.74/35.06 Y0)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)), 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['270'])). 237.74/35.06 tff('272', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => in(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (subset(Y2, Y0) => 237.74/35.06 (subset(Y2, Y1) => 237.74/35.06 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 ( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion( 237.74/35.06 Y0)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)), 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['271'])). 237.74/35.06 tff('273', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (subset(Y2, Y0) => 237.74/35.06 (subset(Y2, Y1) => 237.74/35.06 subset(Y2, binintersect(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion( 237.74/35.06 Y0)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)), 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['272'])). 237.74/35.06 tff('274', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, emptyset), 237.74/35.06 Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion( 237.74/35.06 Y0)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)), 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['273'])). 237.74/35.06 tff('275', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, emptyset), 237.74/35.06 Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion(Y0, 237.74/35.06 Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion(Y0)) => 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)), Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ((!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['274'])). 237.74/35.06 tff('276', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => (binintersect(Y0, Y1) = Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, 237.74/35.06 symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, emptyset), 237.74/35.06 Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion(Y0, 237.74/35.06 Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 ( 237.74/35.06 ??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion(Y0)) => 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)), Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ((!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 ((??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ((??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.06 inference('lazy_cnf_imply', [status(thm)], ['275'])). 237.74/35.06 tff('277', plain, 237.74/35.06 ~ ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y1) => subset(Y1, Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.06 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.06 binunion(binintersect(Y0, Y1), 237.74/35.06 binintersect(Y0, Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, setminus(Y0, Y1)) => 237.74/35.06 (~(in(Y2, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (subset(Y0, Y1) => 237.74/35.06 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.06 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 ((setminus(Y0, Y1) = emptyset) => 237.74/35.06 subset(Y0, Y1)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.06 (!!((^[Y3 : $o]: 237.74/35.06 ((in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.06 (((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => Y3)) => 237.74/35.06 Y3))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (in(Y2, Y1) => 237.74/35.06 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 ((~(in(Y2, Y0))) => 237.74/35.06 ((~(in(Y2, Y1))) => 237.74/35.06 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 in(Y1, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (??((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)))) & 237.74/35.06 (setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y0, 237.74/35.06 setadjoin( 237.74/35.06 Y1, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)) = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 subset( 237.74/35.06 setadjoin(Y1, emptyset), 237.74/35.06 Y0)))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y1, emptyset), 237.74/35.06 powerset(Y0))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 in( 237.74/35.06 setadjoin(Y2, 237.74/35.06 emptyset), 237.74/35.06 powerset( 237.74/35.06 binunion(Y0, 237.74/35.06 Y1))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 setadjoin(Y0, 237.74/35.06 setadjoin(Y1, 237.74/35.06 emptyset))) => 237.74/35.06 ((Y2 = Y1) | 237.74/35.06 (Y2 = Y0)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 subset( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!((^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 powerset( 237.74/35.06 powerset( 237.74/35.06 binunion( 237.74/35.06 Y0, Y1)))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, Y0) => 237.74/35.06 (!!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y3, 237.74/35.06 Y1) => 237.74/35.06 in( 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset)), 237.74/35.06 emptyset)), 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 Y1) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (!!((^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 cartprod( 237.74/35.06 Y0, Y1)) => 237.74/35.06 (??(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (??(( 237.74/35.06 ^[Y4 : $i]: 237.74/35.06 (in(Y4, 237.74/35.06 setunion( 237.74/35.06 Y2)) & 237.74/35.06 (Y2 = 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 emptyset), 237.74/35.06 setadjoin( 237.74/35.06 setadjoin( 237.74/35.06 Y3, 237.74/35.06 setadjoin( 237.74/35.06 Y4, 237.74/35.06 emptyset)), 237.74/35.06 emptyset))))))))))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i]: 237.74/35.06 (in(Y1, 237.74/35.06 setunion(Y0)) => 237.74/35.06 (??((^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) & 237.74/35.06 in(Y1, 237.74/35.06 Y2)))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset( 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)), Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 subset(Y0, 237.74/35.06 setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (setunion( 237.74/35.06 setadjoin(Y0, 237.74/35.06 emptyset)) = 237.74/35.06 Y0)))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ((!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y2) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y2 = Y3))))))))))) => 237.74/35.06 ((??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))))))))))) => 237.74/35.06 ((!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 ((??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 dsetconstr( 237.74/35.06 Y0, Y1)) & 237.74/35.06 (dsetconstr( 237.74/35.06 Y0, Y1) = 237.74/35.06 setadjoin( 237.74/35.06 Y2, 237.74/35.06 emptyset)))))) => 237.74/35.06 (??(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 (in(Y2, 237.74/35.06 Y0) & 237.74/35.06 Y1(Y2)))))))))))) => 237.74/35.06 (!!((^[Y0 : $i]: 237.74/35.06 (!!((^[Y1 : $i > $o]: 237.74/35.06 (!!(( 237.74/35.06 ^[Y2 : $i]: 237.74/35.06 ( 237.74/35.06 in(Y2, 237.74/35.06 Y0) => 237.74/35.06 ( 237.74/35.06 Y1(Y2) => 237.74/35.06 ( 237.74/35.06 ( 237.74/35.06 !!(( 237.74/35.06 ^[Y3 : $i]: 237.74/35.06 (in(Y3, 237.74/35.06 Y0) => 237.74/35.06 (Y1(Y3) => 237.74/35.06 (Y3 = Y2)))))) => 237.74/35.06 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['276'])). 237.74/35.07 tff('278', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, binintersect(Y0, Y1)) => in(Y2, Y1))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.07 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.07 binunion(binintersect(Y0, Y1), 237.74/35.07 binintersect(Y0, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => 237.74/35.07 (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => 237.74/35.07 (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => 237.74/35.07 subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y1, emptyset), 237.74/35.07 Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | 237.74/35.07 (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y0) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, 237.74/35.07 setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 in(Y1, 237.74/35.07 Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)), Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 Y1(Y2) => 237.74/35.07 ( 237.74/35.07 ( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['277'])). 237.74/35.07 tff('279', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((~((??((^[Y2 : $i]: (in(Y2, Y0) & in(Y2, Y1))))))) => 237.74/35.07 (binintersect(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.07 binunion(binintersect(Y0, Y1), 237.74/35.07 binintersect(Y0, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => 237.74/35.07 (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => 237.74/35.07 subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | 237.74/35.07 (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, 237.74/35.07 setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)), Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 (!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['278'])). 237.74/35.07 tff('280', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(binintersect(Y0, Y1), Y1))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.07 binunion(binintersect(Y0, Y1), 237.74/35.07 binintersect(Y0, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => 237.74/35.07 (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => 237.74/35.07 subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | 237.74/35.07 (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, 237.74/35.07 setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)), Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 (!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['279'])). 237.74/35.07 tff('281', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y1, Y0) => (binintersect(Y0, Y1) = Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.07 binunion(binintersect(Y0, Y1), 237.74/35.07 binintersect(Y0, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => 237.74/35.07 subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), 237.74/35.07 Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, 237.74/35.07 Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 Y1(Y2) => 237.74/35.07 ( 237.74/35.07 ( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['280'])). 237.74/35.07 tff('282', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((binintersect(Y0, Y1) = Y0) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.07 binunion(binintersect(Y0, Y1), 237.74/35.07 binintersect(Y0, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => 237.74/35.07 subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), 237.74/35.07 Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, 237.74/35.07 Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y0) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, 237.74/35.07 Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 Y1(Y2) => 237.74/35.07 ( 237.74/35.07 ( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['281'])). 237.74/35.07 tff('283', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (binintersect(Y0, binunion(Y1, Y2)) = 237.74/35.07 binunion(binintersect(Y0, Y1), 237.74/35.07 binintersect(Y0, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => 237.74/35.07 subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), 237.74/35.07 Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion(Y0, 237.74/35.07 Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, 237.74/35.07 Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, 237.74/35.07 Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 ( 237.74/35.07 ( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['282'])). 237.74/35.07 tff('284', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => in(Y2, setminus(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => 237.74/35.07 subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion(Y0, 237.74/35.07 Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y0) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, 237.74/35.07 Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (( 237.74/35.07 !!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 ( 237.74/35.07 ??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['283'])). 237.74/35.07 tff('285', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => in(Y2, Y0))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, emptyset), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion(Y0, 237.74/35.07 Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y0) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 Y1(Y2) => 237.74/35.07 ( 237.74/35.07 Y1(Y3) => 237.74/35.07 ( 237.74/35.07 Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 ((!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['284'])). 237.74/35.07 tff('286', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, setminus(Y0, Y1)) => (~(in(Y2, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin( 237.74/35.07 Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in(setadjoin(Y2, emptyset), 237.74/35.07 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion(Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, 237.74/35.07 Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y0) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y4, 237.74/35.07 Y1) & 237.74/35.07 ( 237.74/35.07 Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 Y1(Y2) => 237.74/35.07 ( 237.74/35.07 Y1(Y3) => 237.74/35.07 ( 237.74/35.07 Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 ((!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y3 = Y2)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['285'])). 237.74/35.07 tff('287', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (subset(Y0, Y1) => (setminus(Y0, Y1) = emptyset)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in(setadjoin(Y2, emptyset), 237.74/35.07 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion(Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, 237.74/35.07 Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, 237.74/35.07 Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod( 237.74/35.07 Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y0) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 ( 237.74/35.07 Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 ( 237.74/35.07 Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 ((!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 Y1(Y3) => 237.74/35.07 ( 237.74/35.07 Y3 = Y2)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 ( 237.74/35.07 in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['286'])). 237.74/35.07 tff('288', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 (in(Y2, Y0) => in(Y2, Y1)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in(setadjoin(Y2, emptyset), 237.74/35.07 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion(Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, 237.74/35.07 Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, 237.74/35.07 Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 powerset( 237.74/35.07 binunion( 237.74/35.07 Y0, Y1)))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 cartprod(Y0, 237.74/35.07 Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y0) & 237.74/35.07 (??((^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 Y1) & 237.74/35.07 (Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 cartprod(Y0, Y1)) => 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 (??(( 237.74/35.07 ^[Y4 : $i]: 237.74/35.07 (in(Y4, 237.74/35.07 setunion( 237.74/35.07 Y2)) & 237.74/35.07 ( 237.74/35.07 Y2 = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 setadjoin( 237.74/35.07 Y4, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, setunion(Y0)) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 in(Y1, Y2)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset( 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)), Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 subset(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(Y0, emptyset)))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (setunion( 237.74/35.07 setadjoin(Y0, emptyset)) = 237.74/35.07 Y0)))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 (Y1(Y3) => 237.74/35.07 (Y2 = Y3))))))))))) => 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 ((??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 (dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 emptyset)))))) => 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) & 237.74/35.07 Y1(Y2)))))))))))) => 237.74/35.07 (!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i > $o]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (Y1(Y2) => 237.74/35.07 ((!!(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 Y0) => 237.74/35.07 ( 237.74/35.07 Y1(Y3) => 237.74/35.07 ( 237.74/35.07 Y3 = Y2)))))) => 237.74/35.07 (??(( 237.74/35.07 ^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1)) & 237.74/35.07 ( 237.74/35.07 dsetconstr( 237.74/35.07 Y0, Y1) = 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.07 inference('lazy_cnf_imply', [status(thm)], ['287'])). 237.74/35.07 tff('289', plain, 237.74/35.07 ~ ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, setminus(Y0, Y1)))) => 237.74/35.07 ((~(in(Y2, Y1))) => (~(in(Y2, Y0)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.07 (!!((^[Y3 : $o]: 237.74/35.07 ((in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.07 (((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => Y3)) => 237.74/35.07 Y3))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (in(Y2, Y1) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 ((~(in(Y2, Y0))) => 237.74/35.07 ((~(in(Y2, Y1))) => 237.74/35.07 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y0, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 in(Y1, 237.74/35.07 setunion( 237.74/35.07 setadjoin(setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (??((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (??((^[Y3 : $i]: 237.74/35.07 (in(Y3, 237.74/35.07 setunion( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)))) & 237.74/35.07 (setadjoin( 237.74/35.07 setadjoin(Y0, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)) = 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (in(Y1, Y0) => 237.74/35.07 in(setadjoin(Y1, emptyset), 237.74/35.07 powerset(Y0))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 in(setadjoin(Y2, emptyset), 237.74/35.07 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, 237.74/35.07 setadjoin(Y0, 237.74/35.07 setadjoin(Y1, emptyset))) => 237.74/35.07 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 binunion(Y0, Y1)))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin(Y2, 237.74/35.07 setadjoin(Y3, 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 subset( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.07 setadjoin( 237.74/35.07 setadjoin( 237.74/35.07 Y2, 237.74/35.07 setadjoin( 237.74/35.07 Y3, 237.74/35.07 emptyset)), 237.74/35.07 emptyset)), 237.74/35.07 powerset( 237.74/35.07 binunion(Y0, 237.74/35.07 Y1))))))))))))))))) => 237.74/35.07 ((!!((^[Y0 : $i]: 237.74/35.07 (!!((^[Y1 : $i]: 237.74/35.07 (!!((^[Y2 : $i]: 237.74/35.07 (in(Y2, Y0) => 237.74/35.07 (!!((^[Y3 : $i]: 237.74/35.07 (in(Y3, Y1) => 237.74/35.07 in( 237.74/35.07 setadjoin( 237.74/35.07 setadjoin(Y2, 237.74/35.07 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion( 237.74/35.08 Y0, Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion( 237.74/35.08 Y0, Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 cartprod(Y0, 237.74/35.08 Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y0) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, 237.74/35.08 Y1) & 237.74/35.08 (Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion(Y2)) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, 237.74/35.08 setunion( 237.74/35.08 Y2)) & 237.74/35.08 (Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, setunion(Y0)) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 in(Y1, Y2)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset( 237.74/35.08 setunion(setadjoin(Y0, emptyset)), 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset(Y0, 237.74/35.08 setunion( 237.74/35.08 setadjoin(Y0, emptyset)))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (setunion( 237.74/35.08 setadjoin(Y0, emptyset)) = 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 ( 237.74/35.08 in(Y3, 237.74/35.08 Y0) => 237.74/35.08 ( 237.74/35.08 Y1(Y2) => 237.74/35.08 ( 237.74/35.08 Y1(Y3) => 237.74/35.08 ( 237.74/35.08 Y2 = Y3))))))))))) => 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 (dsetconstr( 237.74/35.08 Y0, Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 (dsetconstr( 237.74/35.08 Y0, Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2)))))))))))) => 237.74/35.08 (!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (Y1(Y2) => 237.74/35.08 ((!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 Y0) => 237.74/35.08 (Y1(Y3) => 237.74/35.08 (Y3 = Y2)))))) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 (dsetconstr( 237.74/35.08 Y0, Y1) = 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset))))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.08 inference('lazy_cnf_imply', [status(thm)], ['288'])). 237.74/35.08 tff('290', plain, 237.74/35.08 ~ ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.08 (!!((^[Y3 : $o]: 237.74/35.08 ((in(Y2, Y0) => 237.74/35.08 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.08 (((~(in(Y2, Y0))) => 237.74/35.08 (in(Y2, Y1) => Y3)) => 237.74/35.08 Y3))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (in(Y2, Y1) => 237.74/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 ((~(in(Y2, Y1))) => 237.74/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y0, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 in(setadjoin(Y1, emptyset), 237.74/35.08 powerset(Y0))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 in(setadjoin(Y2, emptyset), 237.74/35.08 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset))) => 237.74/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 binunion(Y0, Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, 237.74/35.08 Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion( 237.74/35.08 Y0, Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 cartprod(Y0, 237.74/35.08 Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y0) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 ( 237.74/35.08 in(Y4, 237.74/35.08 Y1) & 237.74/35.08 ( 237.74/35.08 Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion(Y2)) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, 237.74/35.08 setunion( 237.74/35.08 Y2)) & 237.74/35.08 (Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, setunion(Y0)) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 in(Y1, Y2)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset( 237.74/35.08 setunion(setadjoin(Y0, emptyset)), 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset(Y0, 237.74/35.08 setunion(setadjoin(Y0, emptyset)))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (setunion(setadjoin(Y0, emptyset)) = 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 Y0) => 237.74/35.08 ( 237.74/35.08 Y1(Y2) => 237.74/35.08 ( 237.74/35.08 Y1(Y3) => 237.74/35.08 ( 237.74/35.08 Y2 = Y3))))))))))) => 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 (dsetconstr(Y0, 237.74/35.08 Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 (dsetconstr(Y0, 237.74/35.08 Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2)))))))))))) => 237.74/35.08 (!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (Y1(Y2) => 237.74/35.08 ((!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 Y0) => 237.74/35.08 (Y1(Y3) => 237.74/35.08 (Y3 = Y2)))))) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 (dsetconstr( 237.74/35.08 Y0, Y1) = 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.08 inference('lazy_cnf_imply', [status(thm)], ['289'])). 237.74/35.08 tff('291', plain, 237.74/35.08 ~ ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y1) => (~(in(Y2, setminus(Y0, Y1)))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.08 (!!((^[Y3 : $o]: 237.74/35.08 ((in(Y2, Y0) => 237.74/35.08 ((~(in(Y2, Y1))) => Y3)) => 237.74/35.08 (((~(in(Y2, Y0))) => 237.74/35.08 (in(Y2, Y1) => Y3)) => 237.74/35.08 Y3))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (in(Y2, Y1) => 237.74/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 ((~(in(Y2, Y1))) => 237.74/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y0, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 in(setadjoin(Y2, emptyset), 237.74/35.08 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset))) => 237.74/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 binunion(Y0, Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, 237.74/35.08 Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, 237.74/35.08 Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 cartprod(Y0, Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y0) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, 237.74/35.08 Y1) & 237.74/35.08 ( 237.74/35.08 Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion(Y2)) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 ( 237.74/35.08 in(Y4, 237.74/35.08 setunion( 237.74/35.08 Y2)) & 237.74/35.08 ( 237.74/35.08 Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, setunion(Y0)) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 in(Y1, Y2)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset( 237.74/35.08 setunion(setadjoin(Y0, emptyset)), 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset(Y0, 237.74/35.08 setunion(setadjoin(Y0, emptyset)))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (setunion(setadjoin(Y0, emptyset)) = 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y0) => 237.74/35.08 (Y1(Y2) => 237.74/35.08 ( 237.74/35.08 Y1(Y3) => 237.74/35.08 ( 237.74/35.08 Y2 = Y3))))))))))) => 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr(Y0, 237.74/35.08 Y1)) & 237.74/35.08 (dsetconstr(Y0, 237.74/35.08 Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr(Y0, 237.74/35.08 Y1)) & 237.74/35.08 (dsetconstr(Y0, 237.74/35.08 Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2)))))))))))) => 237.74/35.08 (!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (Y1(Y2) => 237.74/35.08 ((!!((^[Y3 : $i]: 237.74/35.08 ( 237.74/35.08 in(Y3, 237.74/35.08 Y0) => 237.74/35.08 ( 237.74/35.08 Y1(Y3) => 237.74/35.08 ( 237.74/35.08 Y3 = Y2)))))) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 ( 237.74/35.08 in(Y3, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 ( 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1) = 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset))))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.08 inference('lazy_cnf_imply', [status(thm)], ['290'])). 237.74/35.08 tff('292', plain, 237.74/35.08 ~ ((!!((^[Y0 : $i]: (!!((^[Y1 : $i]: subset(setminus(Y0, Y1), Y0))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.08 (!!((^[Y3 : $o]: 237.74/35.08 ((in(Y2, Y0) => ((~(in(Y2, Y1))) => Y3)) => 237.74/35.08 (((~(in(Y2, Y0))) => 237.74/35.08 (in(Y2, Y1) => Y3)) => 237.74/35.08 Y3))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 ((~(in(Y2, Y1))) => 237.74/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y0, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 in(setadjoin(Y2, emptyset), 237.74/35.08 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset))) => 237.74/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 binunion(Y0, Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, 237.74/35.08 Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, 237.74/35.08 Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 cartprod(Y0, Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y0) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, Y1) & 237.74/35.08 (Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion(Y2)) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, 237.74/35.08 setunion( 237.74/35.08 Y2)) & 237.74/35.08 ( 237.74/35.08 Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, setunion(Y0)) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset( 237.74/35.08 setunion(setadjoin(Y0, emptyset)), 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 subset(Y0, 237.74/35.08 setunion(setadjoin(Y0, emptyset)))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (setunion(setadjoin(Y0, emptyset)) = 237.74/35.08 Y0)))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y0) => 237.74/35.08 (Y1(Y2) => 237.74/35.08 (Y1(Y3) => 237.74/35.08 ( 237.74/35.08 Y2 = Y3))))))))))) => 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr(Y0, 237.74/35.08 Y1)) & 237.74/35.08 (dsetconstr(Y0, 237.74/35.08 Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 ((??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 dsetconstr(Y0, 237.74/35.08 Y1)) & 237.74/35.08 (dsetconstr(Y0, 237.74/35.08 Y1) = 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset)))))) => 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) & 237.74/35.08 Y1(Y2)))))))))))) => 237.74/35.08 (!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i > $o]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (Y1(Y2) => 237.74/35.08 ((!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 Y0) => 237.74/35.08 ( 237.74/35.08 Y1(Y3) => 237.74/35.08 ( 237.74/35.08 Y3 = Y2)))))) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1)) & 237.74/35.08 ( 237.74/35.08 dsetconstr( 237.74/35.08 Y0, Y1) = 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)))))))))))))))))))))))))))))))))))))))))))))))), 237.74/35.08 inference('lazy_cnf_imply', [status(thm)], ['291'])). 237.74/35.08 tff('293', plain, 237.74/35.08 ~ ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 ((setminus(Y0, Y1) = emptyset) => subset(Y0, Y1)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, symdiff(Y0, Y1)) => 237.74/35.08 (!!((^[Y3 : $o]: 237.74/35.08 ((in(Y2, Y0) => ((~(in(Y2, Y1))) => Y3)) => 237.74/35.08 (((~(in(Y2, Y0))) => (in(Y2, Y1) => Y3)) => 237.74/35.08 Y3))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 ((~(in(Y2, Y0))) => 237.74/35.08 ((~(in(Y2, Y1))) => 237.74/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y0, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 in(Y1, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin(setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (??((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)))) & 237.74/35.08 (setadjoin( 237.74/35.08 setadjoin(Y0, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset)), 237.74/35.08 emptyset)) = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, emptyset)), 237.74/35.08 emptyset))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (in(Y1, Y0) => 237.74/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 in(setadjoin(Y2, emptyset), 237.74/35.08 powerset(binunion(Y0, Y1))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, 237.74/35.08 setadjoin(Y0, 237.74/35.08 setadjoin(Y1, emptyset))) => 237.74/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 binunion(Y0, Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 subset( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin(Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 powerset( 237.74/35.08 powerset( 237.74/35.08 binunion(Y0, 237.74/35.08 Y1)))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, Y0) => 237.74/35.08 (!!((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y1) => 237.74/35.08 in( 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin(Y2, 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset)), 237.74/35.08 emptyset)), 237.74/35.08 cartprod(Y0, Y1)))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, Y0) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, Y1) & 237.74/35.08 (Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 emptyset), 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 237.74/35.08 Y3, 237.74/35.08 setadjoin( 237.74/35.08 Y4, 237.74/35.08 emptyset)), 237.74/35.08 emptyset))))))))))))))))))))) => 237.74/35.08 ((!!((^[Y0 : $i]: 237.74/35.08 (!!((^[Y1 : $i]: 237.74/35.08 (!!((^[Y2 : $i]: 237.74/35.08 (in(Y2, cartprod(Y0, Y1)) => 237.74/35.08 (??((^[Y3 : $i]: 237.74/35.08 (in(Y3, 237.74/35.08 setunion(Y2)) & 237.74/35.08 (??((^[Y4 : $i]: 237.74/35.08 (in(Y4, 237.74/35.08 setunion( 237.74/35.08 Y2)) & 237.74/35.08 (Y2 = 237.74/35.08 setadjoin( 237.74/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset( 238.07/35.08 setunion(setadjoin(Y0, emptyset)), 238.07/35.08 Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, 238.07/35.08 setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = 238.07/35.08 Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, 238.07/35.08 Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, 238.07/35.08 Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 ( 238.07/35.08 Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr( 238.07/35.08 Y0, Y1)) & 238.07/35.08 (dsetconstr( 238.07/35.08 Y0, Y1) = 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset))))))))))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['292'])). 238.07/35.08 tff('294', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, symdiff(Y0, Y1)) => 238.07/35.08 (!!((^[Y3 : $o]: 238.07/35.08 ((in(Y2, Y0) => ((~(in(Y2, Y1))) => Y3)) => 238.07/35.08 (((~(in(Y2, Y0))) => (in(Y2, Y1) => Y3)) => 238.07/35.08 Y3))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 ((~(in(Y2, Y1))) => 238.07/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y0, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion( 238.07/35.08 Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset( 238.07/35.08 setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, 238.07/35.08 setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = 238.07/35.08 Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr( 238.07/35.08 Y0, Y1)) & 238.07/35.08 (dsetconstr( 238.07/35.08 Y0, Y1) = 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset)))))))))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['293'])). 238.07/35.08 tff('295', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 ((~(in(Y2, Y1))) => in(Y2, symdiff(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 ((~(in(Y2, Y1))) => 238.07/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y0, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion( 238.07/35.08 Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset( 238.07/35.08 setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, 238.07/35.08 setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr( 238.07/35.08 Y0, Y1)) & 238.07/35.08 (dsetconstr( 238.07/35.08 Y0, Y1) = 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset))))))))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['294'])). 238.07/35.08 tff('296', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 (in(Y2, Y1) => in(Y2, symdiff(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 ((~(in(Y2, Y1))) => 238.07/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y0, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion( 238.07/35.08 Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), 238.07/35.08 Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, 238.07/35.08 setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr( 238.07/35.08 Y0, Y1)) & 238.07/35.08 (dsetconstr( 238.07/35.08 Y0, Y1) = 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset)))))))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['295'])). 238.07/35.08 tff('297', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (in(Y2, Y1) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 ((~(in(Y2, Y1))) => 238.07/35.08 (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y0, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), 238.07/35.08 Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, 238.07/35.08 setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr( 238.07/35.08 Y0, Y1)) & 238.07/35.08 (dsetconstr( 238.07/35.08 Y0, Y1) = 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset))))))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['296'])). 238.07/35.08 tff('298', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 ((~(in(Y2, Y0))) => 238.07/35.08 ((~(in(Y2, Y1))) => (~(in(Y2, symdiff(Y0, Y1))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y0, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), 238.07/35.08 Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, 238.07/35.08 setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr( 238.07/35.08 Y0, Y1)) & 238.07/35.08 (dsetconstr( 238.07/35.08 Y0, Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)))))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['297'])). 238.07/35.08 tff('299', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: in(Y1, setadjoin(Y0, setadjoin(Y1, emptyset))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y0, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, 238.07/35.08 setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr( 238.07/35.08 Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, 238.07/35.08 Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset))))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['298'])). 238.07/35.08 tff('300', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y0, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, 238.07/35.08 Y1)) & 238.07/35.08 (dsetconstr(Y0, 238.07/35.08 Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['299'])). 238.07/35.08 tff('301', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 in(Y1, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin(setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset( 238.07/35.08 binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin( 238.07/35.08 Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, 238.07/35.08 Y1)) & 238.07/35.08 (dsetconstr(Y0, 238.07/35.08 Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset))))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['300'])). 238.07/35.08 tff('302', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, 238.07/35.08 setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => 238.07/35.08 (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, 238.07/35.08 Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['301'])). 238.07/35.08 tff('303', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 setunion( 238.07/35.08 setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)))) & 238.07/35.08 (setadjoin(setadjoin(Y0, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y0, 238.07/35.08 setadjoin(Y1, emptyset)), 238.07/35.08 emptyset)) = 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin( 238.07/35.08 Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset))))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['302'])). 238.07/35.08 tff('304', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => subset(setadjoin(Y1, emptyset), Y0)))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => 238.07/35.08 in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, 238.07/35.08 setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['303'])). 238.07/35.08 tff('305', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, Y0) => in(setadjoin(Y1, emptyset), powerset(Y0))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset))))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['304'])). 238.07/35.08 tff('306', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 in(setadjoin(Y2, emptyset), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset)))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['305'])). 238.07/35.08 tff('307', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, setadjoin(Y0, setadjoin(Y1, emptyset))) => 238.07/35.08 ((Y2 = Y1) | (Y2 = Y0)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y3, emptyset))))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['306'])). 238.07/35.08 tff('308', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(Y2, setadjoin(Y3, emptyset)), 238.07/35.08 binunion(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (in(Y1, setunion(Y0)) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.08 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.08 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.08 (??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 ((??((^[Y2 : $i]: 238.07/35.08 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y2, emptyset)))))) => 238.07/35.08 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.08 (!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i > $o]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (Y1(Y2) => 238.07/35.08 ((!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) => 238.07/35.08 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, 238.07/35.08 dsetconstr(Y0, Y1)) & 238.07/35.08 (dsetconstr(Y0, Y1) = 238.07/35.08 setadjoin(Y3, emptyset)))))))))))))))))))))))))))))))), 238.07/35.08 inference('lazy_cnf_imply', [status(thm)], ['307'])). 238.07/35.08 tff('309', plain, 238.07/35.08 ~ ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(Y2, setadjoin(Y3, emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 subset( 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin(setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), 238.07/35.08 powerset( 238.07/35.08 powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, Y0) => 238.07/35.08 (!!((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y1) => 238.07/35.08 in( 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y2, 238.07/35.08 setadjoin(Y3, emptyset)), 238.07/35.08 emptyset)), cartprod(Y0, Y1)))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, Y0) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, Y1) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, emptyset), 238.07/35.08 setadjoin( 238.07/35.08 setadjoin(Y3, 238.07/35.08 setadjoin(Y4, 238.07/35.08 emptyset)), 238.07/35.08 emptyset))))))))))))))))))))) => 238.07/35.08 ((!!((^[Y0 : $i]: 238.07/35.08 (!!((^[Y1 : $i]: 238.07/35.08 (!!((^[Y2 : $i]: 238.07/35.08 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.08 (??((^[Y3 : $i]: 238.07/35.08 (in(Y3, setunion(Y2)) & 238.07/35.08 (??((^[Y4 : $i]: 238.07/35.08 (in(Y4, setunion(Y2)) & 238.07/35.08 (Y2 = 238.07/35.08 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, 238.07/35.09 emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset))))))))))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['308'])). 238.07/35.09 tff('310', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 subset( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), 238.07/35.09 powerset(binunion(Y0, Y1))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), 238.07/35.09 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), 238.07/35.09 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), cartprod(Y0, Y1)))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, Y1) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, 238.07/35.09 emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, setunion(Y2)) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, setunion(Y2)) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, 238.07/35.09 emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset)))))))))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['309'])). 238.07/35.09 tff('311', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), 238.07/35.09 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), 238.07/35.09 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), cartprod(Y0, Y1)))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, Y1) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, 238.07/35.09 emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, setunion(Y2)) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, setunion(Y2)) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, 238.07/35.09 emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset))))))))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['310'])). 238.07/35.09 tff('312', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), 238.07/35.09 powerset(powerset(binunion(Y0, Y1)))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), cartprod(Y0, Y1)))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, Y1) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, setunion(Y2)) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, setunion(Y2)) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, 238.07/35.09 emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset)))))))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['311'])). 238.07/35.09 tff('313', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y1) => 238.07/35.09 in( 238.07/35.09 setadjoin(setadjoin(Y2, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y2, 238.07/35.09 setadjoin(Y3, emptyset)), 238.07/35.09 emptyset)), cartprod(Y0, Y1)))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, Y1) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, setunion(Y2)) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, setunion(Y2)) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset))))))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['312'])). 238.07/35.09 tff('314', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, Y1) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, setunion(Y2)) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, setunion(Y2)) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset)))))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['313'])). 238.07/35.09 tff('315', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, cartprod(Y0, Y1)) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, setunion(Y2)) & 238.07/35.09 (??((^[Y4 : $i]: 238.07/35.09 (in(Y4, setunion(Y2)) & 238.07/35.09 (Y2 = 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, emptyset), 238.07/35.09 setadjoin( 238.07/35.09 setadjoin(Y3, 238.07/35.09 setadjoin(Y4, emptyset)), 238.07/35.09 emptyset))))))))))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset))))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['314'])). 238.07/35.09 tff('316', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, setunion(Y0)) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & in(Y1, Y2)))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset)))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['315'])). 238.07/35.09 tff('317', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: subset(setunion(setadjoin(Y0, emptyset)), Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset))))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['316'])). 238.07/35.09 tff('318', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: subset(Y0, setunion(setadjoin(Y0, emptyset)))))) => 238.07/35.09 ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset)))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['317'])). 238.07/35.09 tff('319', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: (setunion(setadjoin(Y0, emptyset)) = Y0)))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset))))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['318'])). 238.07/35.09 tff('320', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = setadjoin(Y2, emptyset)))))))))))))) => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset)))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['319'])). 238.07/35.09 tff('321', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = setadjoin(Y2, emptyset)))))) => 238.07/35.09 (??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2)))))))))))) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset))))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['320'])). 238.07/35.09 tff('322', plain, 238.07/35.09 ~ (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (Y1(Y2) => 238.07/35.09 ((!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => (Y1(Y3) => (Y3 = Y2)))))) => 238.07/35.09 (??((^[Y3 : $i]: 238.07/35.09 (in(Y3, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = 238.07/35.09 setadjoin(Y3, emptyset)))))))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['321'])). 238.07/35.09 tff('323', plain, 238.07/35.09 ~ (!!((^[Y0 : $i > $o]: 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, '#sk807') => 238.07/35.09 (Y0(Y1) => 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, '#sk807') => (Y0(Y2) => (Y2 = Y1)))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr('#sk807', Y0)) & 238.07/35.09 (dsetconstr('#sk807', Y0) = 238.07/35.09 setadjoin(Y2, emptyset))))))))))))))), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['322'])). 238.07/35.09 tff('324', plain, 238.07/35.09 ~ (!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, '#sk807') => 238.07/35.09 ('#sk813'(Y0) => 238.07/35.09 ((!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, '#sk807') => ('#sk813'(Y1) => (Y1 = Y0)))))) => 238.07/35.09 (??((^[Y1 : $i]: 238.07/35.09 (in(Y1, dsetconstr('#sk807', '#sk813')) & 238.07/35.09 (dsetconstr('#sk807', '#sk813') = 238.07/35.09 setadjoin(Y1, emptyset)))))))))))), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['323'])). 238.07/35.09 tff('325', plain, 238.07/35.09 ~ (in('#sk823', '#sk807') => 238.07/35.09 ('#sk813'('#sk823') => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, '#sk807') => ('#sk813'(Y0) => (Y0 = '#sk823')))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr('#sk807', '#sk813')) & 238.07/35.09 (dsetconstr('#sk807', '#sk813') = setadjoin(Y0, emptyset))))))))), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['324'])). 238.07/35.09 tff('326', plain, 238.07/35.09 ~ ('#sk813'('#sk823') => 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, '#sk807') => ('#sk813'(Y0) => (Y0 = '#sk823')))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr('#sk807', '#sk813')) & 238.07/35.09 (dsetconstr('#sk807', '#sk813') = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['325'])). 238.07/35.09 tff('327', plain, '#sk813'('#sk823'), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['326'])). 238.07/35.09 tff('328', plain, in('#sk823', '#sk807'), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['325'])). 238.07/35.09 tff('329', plain, 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (!!((^[Y1 : $i > $o]: 238.07/35.09 ((!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, Y0) => 238.07/35.09 (!!((^[Y3 : $i]: 238.07/35.09 (in(Y3, Y0) => 238.07/35.09 (Y1(Y2) => (Y1(Y3) => (Y2 = Y3))))))))))) => 238.07/35.09 ((??((^[Y2 : $i]: (in(Y2, Y0) & Y1(Y2))))) => 238.07/35.09 (??((^[Y2 : $i]: 238.07/35.09 (in(Y2, dsetconstr(Y0, Y1)) & 238.07/35.09 (dsetconstr(Y0, Y1) = setadjoin(Y2, emptyset)))))))))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['320'])). 238.07/35.09 tff('330', plain, 238.07/35.09 ![X1]: 238.07/35.09 (!!((^[Y0 : $i > $o]: 238.07/35.09 ((!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, X1) => 238.07/35.09 (!!((^[Y2 : $i]: 238.07/35.09 (in(Y2, X1) => 238.07/35.09 (Y0(Y1) => (Y0(Y2) => (Y1 = Y2))))))))))) => 238.07/35.09 ((??((^[Y1 : $i]: (in(Y1, X1) & Y0(Y1))))) => 238.07/35.09 (??((^[Y1 : $i]: 238.07/35.09 (in(Y1, dsetconstr(X1, Y0)) & 238.07/35.09 (dsetconstr(X1, Y0) = setadjoin(Y1, emptyset))))))))))), 238.07/35.09 inference('lazy_cnf_forall', [status(thm)], ['329'])). 238.07/35.09 tff('331', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ((!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, X1) => 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, X1) => (X2(Y0) => (X2(Y1) => (Y0 = Y1))))))))))) => 238.07/35.09 ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_forall', [status(thm)], ['330'])). 238.07/35.09 tff('332', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, X1) => 238.07/35.09 (!!((^[Y1 : $i]: 238.07/35.09 (in(Y1, X1) => (X2(Y0) => (X2(Y1) => (Y0 = Y1))))))))))) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['331'])). 238.07/35.09 tff('333', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (in('#sk819'(X1, X2), X1) => 238.07/35.09 (!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, X1) => 238.07/35.09 (X2('#sk819'(X1, X2)) => 238.07/35.09 (X2(Y0) => ('#sk819'(X1, X2) = Y0)))))))) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['332'])). 238.07/35.09 tff('334', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( in('#sk819'(X1, X2), X1) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['333'])). 238.07/35.09 tff('335', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))) 238.07/35.09 | in('#sk819'(X1, X2), X1)), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['334'])). 238.07/35.09 tff('336', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( '#form834'(X1, X2) | ~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0)))))), 238.07/35.09 define([status(thm)])). 238.07/35.09 tff('337', plain, 238.07/35.09 ![X1, X2 : $i > $o, X3]: (~ (in(X3, X1) & X2(X3)) | '#form834'(X1, X2)), 238.07/35.09 inference('lazy_cnf_forall', [status(thm)], ['336'])). 238.07/35.09 tff('338', plain, 238.07/35.09 ![X1, X2 : $i > $o, X3]: (~ in(X3, X1) | ~ X2(X3) | '#form834'(X1, X2)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['337'])). 238.07/35.09 tff('339', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, X1) => 238.07/35.09 (X2('#sk819'(X1, X2)) => (X2(Y0) => ('#sk819'(X1, X2) = Y0))))))) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['333'])). 238.07/35.09 tff('340', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (in('#sk845'(X1, X2), X1) => 238.07/35.09 (X2('#sk819'(X1, X2)) => 238.07/35.09 (X2('#sk845'(X1, X2)) => ('#sk819'(X1, X2) = '#sk845'(X1, X2))))) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['339'])). 238.07/35.09 tff('341', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (X2('#sk819'(X1, X2)) => 238.07/35.09 (X2('#sk845'(X1, X2)) => ('#sk819'(X1, X2) = '#sk845'(X1, X2)))) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['340'])). 238.07/35.09 tff('342', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (X2('#sk845'(X1, X2)) => ('#sk819'(X1, X2) = '#sk845'(X1, X2))) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['341'])). 238.07/35.09 tff('343', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( X2('#sk819'(X1, X2)) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['341'])). 238.07/35.09 tff('344', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form913'(X1, X2) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 define([status(thm)])). 238.07/35.09 tff('345', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( '#form913'(X1, (^[Y0 : $i]: X2(Y0))) 238.07/35.09 | ~ (X2('#sk845'(X1, X2)) => ('#sk819'(X1, X2) = '#sk845'(X1, X2)))), 238.07/35.09 inference('renaming', [status(thm)], ['342', '344'])). 238.07/35.09 tff('346', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( '#form913'(X1, X2) 238.07/35.09 | ~ (X2('#sk845'(X1, X2)) => ('#sk819'(X1, X2) = '#sk845'(X1, X2)))), 238.07/35.09 inference('ho_norm', [status(thm)], ['345'])). 238.07/35.09 tff('347', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ('#sk819'(X1, X2) != '#sk845'(X1, X2) | '#form913'(X1, X2)), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['346'])). 238.07/35.09 tff('348', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))) 238.07/35.09 | in('#sk819'(X1, X2), X1)), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['334'])). 238.07/35.09 tff('349', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( '#form834'(X1, X2) | ~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0)))))), 238.07/35.09 define([status(thm)])). 238.07/35.09 tff('350', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form834'(X1, (^[Y0 : $i]: X2(Y0))) 238.07/35.09 | in('#sk819'(X1, X2), X1) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset))))))), 238.07/35.09 inference('renaming', [status(thm)], ['348', '349'])). 238.07/35.09 tff('351', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form834'(X1, X2) 238.07/35.09 | in('#sk819'(X1, X2), X1) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset))))))), 238.07/35.09 inference('ho_norm', [status(thm)], ['350'])). 238.07/35.09 tff('352', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( (in('#sk877'(X1, X2), dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin('#sk877'(X1, X2), emptyset))) 238.07/35.09 | in('#sk819'(X1, X2), X1) 238.07/35.09 | ~ '#form834'(X1, X2)), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['351'])). 238.07/35.09 tff('353', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (dsetconstr(X1, X2) = setadjoin('#sk877'(X1, X2), emptyset) 238.07/35.09 | ~ '#form834'(X1, X2) 238.07/35.09 | in('#sk819'(X1, X2), X1)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['352'])). 238.07/35.09 tff('354', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( in('#sk877'(X1, X2), dsetconstr(X1, X2)) 238.07/35.09 | ~ '#form834'(X1, X2) 238.07/35.09 | in('#sk819'(X1, X2), X1)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['352'])). 238.07/35.09 tff('355', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( X2('#sk819'(X1, X2)) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['341'])). 238.07/35.09 tff('356', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form913'(X1, X2) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 define([status(thm)])). 238.07/35.09 tff('357', plain, 238.07/35.09 ![X1, X2 : $i > $o]: ( '#form913'(X1, X2) | X2('#sk819'(X1, X2))), 238.07/35.09 inference('renaming', [status(thm)], ['355', '356'])). 238.07/35.09 tff('358', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form913'(X1, X2) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 define([status(thm)])). 238.07/35.09 tff('359', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))) 238.07/35.09 | ~ '#form913'(X1, X2)), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['358'])). 238.07/35.09 tff('360', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( '#form834'(X1, X2) | ~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0)))))), 238.07/35.09 define([status(thm)])). 238.07/35.09 tff('361', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form834'(X1, (^[Y0 : $i]: X2(Y0))) 238.07/35.09 | ~ '#form913'(X1, X2) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset))))))), 238.07/35.09 inference('renaming', [status(thm)], ['359', '360'])). 238.07/35.09 tff('362', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form834'(X1, X2) 238.07/35.09 | ~ '#form913'(X1, X2) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset))))))), 238.07/35.09 inference('ho_norm', [status(thm)], ['361'])). 238.07/35.09 tff('363', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( (in('#sk877'(X1, X2), dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin('#sk877'(X1, X2), emptyset))) 238.07/35.09 | ~ '#form913'(X1, X2) 238.07/35.09 | ~ '#form834'(X1, X2)), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['362'])). 238.07/35.09 tff('364', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (dsetconstr(X1, X2) = setadjoin('#sk877'(X1, X2), emptyset) 238.07/35.09 | ~ '#form834'(X1, X2) 238.07/35.09 | ~ '#form913'(X1, X2)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['363'])). 238.07/35.09 tff('365', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( in('#sk877'(X1, X2), dsetconstr(X1, X2)) 238.07/35.09 | ~ '#form834'(X1, X2) 238.07/35.09 | ~ '#form913'(X1, X2)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['363'])). 238.07/35.09 tff('366', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( in('#sk845'(X1, X2), X1) 238.07/35.09 | ((??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['340'])). 238.07/35.09 tff('367', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0))))) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset)))))) 238.07/35.09 | in('#sk845'(X1, X2), X1)), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['366'])). 238.07/35.09 tff('368', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( '#form834'(X1, X2) | ~ (??((^[Y0 : $i]: (in(Y0, X1) & X2(Y0)))))), 238.07/35.09 define([status(thm)])). 238.07/35.09 tff('369', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form834'(X1, (^[Y0 : $i]: X2(Y0))) 238.07/35.09 | in('#sk845'(X1, X2), X1) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset))))))), 238.07/35.09 inference('renaming', [status(thm)], ['367', '368'])). 238.07/35.09 tff('370', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (~ '#form834'(X1, X2) 238.07/35.09 | in('#sk845'(X1, X2), X1) 238.07/35.09 | (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin(Y0, emptyset))))))), 238.07/35.09 inference('ho_norm', [status(thm)], ['369'])). 238.07/35.09 tff('371', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( (in('#sk877'(X1, X2), dsetconstr(X1, X2)) & 238.07/35.09 (dsetconstr(X1, X2) = setadjoin('#sk877'(X1, X2), emptyset))) 238.07/35.09 | in('#sk845'(X1, X2), X1) 238.07/35.09 | ~ '#form834'(X1, X2)), 238.07/35.09 inference('lazy_cnf_exists', [status(thm)], ['370'])). 238.07/35.09 tff('372', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 (dsetconstr(X1, X2) = setadjoin('#sk877'(X1, X2), emptyset) 238.07/35.09 | ~ '#form834'(X1, X2) 238.07/35.09 | in('#sk845'(X1, X2), X1)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['371'])). 238.07/35.09 tff('373', plain, 238.07/35.09 ![X1, X2 : $i > $o]: 238.07/35.09 ( in('#sk877'(X1, X2), dsetconstr(X1, X2)) 238.07/35.09 | ~ '#form834'(X1, X2) 238.07/35.09 | in('#sk845'(X1, X2), X1)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['371'])). 238.07/35.09 tff('374', plain, 238.07/35.09 ~ ((!!((^[Y0 : $i]: 238.07/35.09 (in(Y0, '#sk807') => ('#sk813'(Y0) => (Y0 = '#sk823')))))) => 238.07/35.09 (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr('#sk807', '#sk813')) & 238.07/35.09 (dsetconstr('#sk807', '#sk813') = setadjoin(Y0, emptyset))))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['326'])). 238.07/35.09 tff('375', plain, 238.07/35.09 ~ (??((^[Y0 : $i]: 238.07/35.09 (in(Y0, dsetconstr('#sk807', '#sk813')) & 238.07/35.09 (dsetconstr('#sk807', '#sk813') = setadjoin(Y0, emptyset)))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['374'])). 238.07/35.09 tff('376', plain, 238.07/35.09 ![X1]: 238.07/35.09 ~ (in(X1, dsetconstr('#sk807', '#sk813')) & 238.07/35.09 (dsetconstr('#sk807', '#sk813') = setadjoin(X1, emptyset))), 238.07/35.09 inference('lazy_cnf_forall', [status(thm)], ['375'])). 238.07/35.09 tff('377', plain, 238.07/35.09 ![X1]: 238.07/35.09 (~ in(X1, dsetconstr('#sk807', '#sk813')) 238.07/35.09 | dsetconstr('#sk807', '#sk813') != setadjoin(X1, emptyset)), 238.07/35.09 inference('lazy_cnf_and', [status(thm)], ['376'])). 238.07/35.09 tff('378', plain, 238.07/35.09 ![X1, X2 : $i > $o]: ( X2('#sk845'(X1, X2)) | '#form913'(X1, X2)), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['346'])). 238.07/35.09 tff('379', plain, 238.07/35.09 (!!((^[Y0 : $i]: (in(Y0, '#sk807') => ('#sk813'(Y0) => (Y0 = '#sk823')))))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['374'])). 238.07/35.09 tff('380', plain, 238.07/35.09 ![X1]: (in(X1, '#sk807') => ('#sk813'(X1) => (X1 = '#sk823'))), 238.07/35.09 inference('lazy_cnf_forall', [status(thm)], ['379'])). 238.07/35.09 tff('381', plain, 238.07/35.09 ![X1]: (~ in(X1, '#sk807') | ('#sk813'(X1) => (X1 = '#sk823'))), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['380'])). 238.07/35.09 tff('382', plain, 238.07/35.09 ![X1]: (~ '#sk813'(X1) | X1 = '#sk823' | ~ in(X1, '#sk807')), 238.07/35.09 inference('lazy_cnf_imply', [status(thm)], ['381'])). 238.07/35.09 tff('383', plain, $false, 238.07/35.09 inference('eprover', [status(thm)], 238.07/35.09 ['327', '328', '338', '347', '353', '354', '357', '364', 238.07/35.09 '365', '372', '373', '377', '378', '382'])). 238.07/35.09 238.07/35.09 % SZS output end Refutation 238.07/35.09 238.07/35.09 238.07/35.09 % /export/starexec/sandbox/solver/bin/lams/c.preprocess2.sh running for 21s 238.07/35.09 % Terminating... 238.07/35.15 % Runner terminated. 238.07/35.17 % Zipperpin 1.5 exiting 238.07/35.18 EOF