0.00/0.05	% Problem  : theBenchmark.p : TPTP v0.0.0. Released v0.0.0.
0.00/0.11	% Command  : python3 /export/starexec/sandbox2/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox2/tmp/tmp.Mer5sRNpi3 true
0.21/0.47	% Computer : n018.cluster.edu
0.21/0.47	% Model    : x86_64 x86_64
0.21/0.47	% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
0.21/0.47	% Memory   : 8046.5625MB
0.21/0.47	% OS       : Linux 6.8.0-71-generic
0.21/0.48	% CPULimit : 1440
0.21/0.48	% WCLimit  : 180
0.21/0.48	% DateTime : Mon Jul 27 12:14:23 UTC 2026
0.21/0.48	% CPUTime  : 
0.21/0.48	% Running portfolio for 1440 s
0.21/0.48	% File         : /export/starexec/sandbox2/benchmark/theBenchmark.p
0.21/0.48	% Number of cores: 8
0.21/0.49	% Python version: Python 3.12.3
0.21/0.49	% Running in HO mode
0.45/0.92	% Total configuration time : 828
0.45/0.92	% Estimated wc time : 1656
0.45/0.92	% Estimated cpu time (8 cpus) : 207.0
0.45/1.02	% /export/starexec/sandbox2/solver/bin/lams/40_c.s.sh running for 80s
2.14/1.13	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif4.sh running for 80s
2.14/1.13	% /export/starexec/sandbox2/solver/bin/lams/15_e_short1.sh running for 30s
2.14/1.13	% /export/starexec/sandbox2/solver/bin/lams/40_c_ic.sh running for 80s
2.14/1.13	% /export/starexec/sandbox2/solver/bin/lams/40_noforms.sh running for 90s
2.14/1.13	% /export/starexec/sandbox2/solver/bin/lams/20_acsne_simpl.sh running for 40s
2.14/1.13	% /export/starexec/sandbox2/solver/bin/lams/40_b.comb.sh running for 70s
2.14/1.18	% /export/starexec/sandbox2/solver/bin/lams/30_sp5.sh running for 60s
2.14/1.21	% /export/starexec/sandbox2/solver/bin/lams/30_b.l.sh running for 90s
12.37/2.47	% Solved by lams/30_b.l.sh.
12.37/2.47	% done 0 iterations in 0.880s
12.37/2.47	% SZS status Theorem for '/export/starexec/sandbox2/benchmark/theBenchmark.p'
12.37/2.47	% SZS output start Refutation
12.37/2.47	thf(term_type, type, term: $tType).
12.37/2.47	thf(subst_type, type, subst: $tType).
12.37/2.47	thf(d_term_type, type, d_term: $tType).
12.37/2.47	thf(d_subst_type, type, d_subst: $tType).
12.37/2.47	thf(axmap_type, type, axmap: $o).
12.37/2.47	thf(hoasinduction_lem3a_type, type, hoasinduction_lem3a: $o).
12.37/2.47	thf(hoasapnotvar_gthm_type, type, hoasapnotvar_gthm: $o).
12.37/2.47	thf(pushprop_lthm_orig_type, type, pushprop_lthm_orig: $o).
12.37/2.47	thf(termmset_gthm_type, type, termmset_gthm: $o).
12.37/2.47	thf(axclos_type, type, axclos: $o).
12.37/2.47	thf(lam_type, type, lam: term > term).
12.37/2.47	thf(lamnotap_type, type, lamnotap: $o).
12.37/2.47	thf(hoasinduction_lem3aa_type, type, hoasinduction_lem3aa: $o).
12.37/2.47	thf(hoaslamnotvar_gthm_type, type, hoaslamnotvar_gthm: $o).
12.37/2.47	thf(axvarcons_type, type, axvarcons: $o).
12.37/2.47	thf(hoaslamnotvar_lthm_type, type, hoaslamnotvar_lthm: $o).
12.37/2.47	thf(d2term_type, type, d2term: d_term > term).
12.37/2.47	thf(hoasinduction_no_psi_cond_lthm_type, type, hoasinduction_no_psi_cond_lthm: 
12.37/2.47	    $o).
12.37/2.47	thf(substmonoid_type, type, substmonoid: $o).
12.37/2.47	thf(hoasinduction_lem3a_gthm_type, type, hoasinduction_lem3a_gthm: $o).
12.37/2.47	thf(substmonoid_gthm_type, type, substmonoid_gthm: $o).
12.37/2.47	thf(d_id_type, type, d_id: d_subst).
12.37/2.47	thf(pushprop_gthm_type, type, pushprop_gthm: $o).
12.37/2.47	thf(hoasinduction_lem3v2_type, type, hoasinduction_lem3v2: $o).
12.37/2.47	thf(pushprop_lem1v2_type, type, pushprop_lem1v2: $o).
12.37/2.47	thf(push_type, type, push: term > subst > subst).
12.37/2.47	thf(hoaslamnotap_lthm_type, type, hoaslamnotap_lthm: $o).
12.37/2.47	thf('#sk2_type', type, '#sk2': subst > d_subst).
12.37/2.47	thf(axshiftcons_type, type, axshiftcons: $o).
12.37/2.47	thf(hoasinduction_lem1v2_type, type, hoasinduction_lem1v2: $o).
12.37/2.47	thf(hoasapinj1_lthm_type, type, hoasapinj1_lthm: $o).
12.37/2.47	thf(hoasapinj1_type, type, hoasapinj1: $o).
12.37/2.47	thf(hoasinduction_p_and_p_prime_type, type, hoasinduction_p_and_p_prime: 
12.37/2.47	    (subst > term > subst > $o) > (term > $o) > $o).
12.37/2.47	thf(axapp_type, type, axapp: $o).
12.37/2.47	thf(hoasinduction_lem3_lthm_type, type, hoasinduction_lem3_lthm: $o).
12.37/2.47	thf(hoasinduction_lem3v2_lthm_type, type, hoasinduction_lem3v2_lthm: $o).
12.37/2.47	thf(pushprop_lem1v2_gthm_type, type, pushprop_lem1v2_gthm: $o).
12.37/2.47	thf(shinj_type, type, shinj: $o).
12.37/2.47	thf(hoasap_type, type, hoasap: subst > term > subst > term > term).
12.37/2.47	thf(hoasinduction_gthm_type, type, hoasinduction_gthm: $o).
12.37/2.47	thf(hoasinduction_lem3b_type, type, hoasinduction_lem3b: $o).
12.37/2.47	thf(hoaslaminj_type, type, hoaslaminj: $o).
12.37/2.47	thf(induction2_lthm_type, type, induction2_lthm: $o).
12.37/2.47	thf(induction2_gthm_type, type, induction2_gthm: $o).
12.37/2.47	thf(hoasinduction_lem2_gthm_type, type, hoasinduction_lem2_gthm: $o).
12.37/2.47	thf(one_type, type, one: term).
12.37/2.47	thf(pushprop_lem2v2_lthm_type, type, pushprop_lem2v2_lthm: $o).
12.37/2.47	thf(id_type, type, id: subst).
12.37/2.47	thf(comp_type, type, comp: subst > subst > subst).
12.37/2.47	thf('#sk1_type', type, '#sk1': term > d_term).
12.37/2.47	thf(hoaslamnotap_type, type, hoaslamnotap: $o).
12.37/2.47	thf(induction2_type, type, induction2: $o).
12.37/2.47	thf(axvarid_type, type, axvarid: $o).
12.37/2.47	thf(axvarshift_type, type, axvarshift: $o).
12.37/2.47	thf(hoaslamnotap_gthm_type, type, hoaslamnotap_gthm: $o).
12.37/2.47	thf(induction2lem_type, type, induction2lem: $o).
12.37/2.47	thf(hoasinduction_lem1_gthm_type, type, hoasinduction_lem1_gthm: $o).
12.37/2.47	thf(sh_type, type, sh: subst).
12.37/2.47	thf(hoasinduction_lem2v2_type, type, hoasinduction_lem2v2: $o).
12.37/2.47	thf('#sk4_type', type, '#sk4': subst).
12.37/2.47	thf(laminj_type, type, laminj: $o).
12.37/2.47	thf(hoasinduction_lem3aa_lthm_type, type, hoasinduction_lem3aa_lthm: $o).
12.37/2.47	thf(ulamvarind_type, type, ulamvarind: $o).
12.37/2.47	thf(pushprop_lem2v2_type, type, pushprop_lem2v2: $o).
12.37/2.47	thf(hoasinduction_lthm_3_type, type, hoasinduction_lthm_3: $o).
12.37/2.47	thf(hoasinduction_lem3v2_f_lthm_type, type, hoasinduction_lem3v2_f_lthm: $o).
12.37/2.47	thf(apinj2_type, type, apinj2: $o).
12.37/2.47	thf(hoasapinj2_lthm_type, type, hoasapinj2_lthm: $o).
12.37/2.47	thf(ulamvarsh_type, type, ulamvarsh: $o).
12.37/2.47	thf(hoasinduction_lem3v2a_lthm_type, type, hoasinduction_lem3v2a_lthm: $o).
12.37/2.47	thf(hoasinduction_lem3a_lthm_type, type, hoasinduction_lem3a_lthm: $o).
12.37/2.47	thf(pushprop_lthm_type, type, pushprop_lthm: $o).
12.37/2.47	thf(hoasapinj1_gthm_type, type, hoasapinj1_gthm: $o).
12.37/2.47	thf(hoasinduction_lem0_lthm_type, type, hoasinduction_lem0_lthm: $o).
12.37/2.47	thf(hoasinduction_lem3b_lthm_type, type, hoasinduction_lem3b_lthm: $o).
12.37/2.47	thf(lamnotvar_type, type, lamnotvar: $o).
12.37/2.47	thf(apnotvar_type, type, apnotvar: $o).
12.37/2.47	thf(pushprop_p_and_p_prime_type, type, pushprop_p_and_p_prime: term > 
12.37/2.47	                                                               subst > 
12.37/2.47	                                                               (term > $o) > 
12.37/2.47	                                                               (term > $o) > $o).
12.37/2.47	thf(hoasapinj2_gthm_type, type, hoasapinj2_gthm: $o).
12.37/2.47	thf(d_one_type, type, d_one: d_term).
12.37/2.47	thf(pushprop_lem1_type, type, pushprop_lem1: $o).
12.37/2.47	thf(pushprop_type, type, pushprop: $o).
12.37/2.47	thf(hoasinduction_lem1_lthm_type, type, hoasinduction_lem1_lthm: $o).
12.37/2.47	thf(hoasinduction_lem3_gthm_type, type, hoasinduction_lem3_gthm: $o).
12.37/2.47	thf(sub_type, type, sub: term > subst > term).
12.37/2.47	thf(apinj1_type, type, apinj1: $o).
12.37/2.47	thf(axidl_type, type, axidl: $o).
12.37/2.47	thf(hoasinduction_type, type, hoasinduction: $o).
12.37/2.47	thf(ap_type, type, ap: term > term > term).
12.37/2.47	thf(termmset_type, type, termmset: $o).
12.37/2.47	thf(hoasapinj2_type, type, hoasapinj2: $o).
12.37/2.47	thf(hoasinduction_lem1_type, type, hoasinduction_lem1: $o).
12.37/2.47	thf(pushprop_lem3v2_lthm_type, type, pushprop_lem3v2_lthm: $o).
12.37/2.47	thf(hoasinduction_lem3v2a_type, type, hoasinduction_lem3v2a: $o).
12.37/2.47	thf(hoasapnotvar_type, type, hoasapnotvar: $o).
12.37/2.47	thf(var_type, type, var: term > $o).
12.37/2.47	thf(pushprop_lem1_lthm_type, type, pushprop_lem1_lthm: $o).
12.37/2.47	thf(induction2lem_lthm_type, type, induction2lem_lthm: $o).
12.37/2.47	thf(pushprop_lem0_lthm_type, type, pushprop_lem0_lthm: $o).
12.37/2.47	thf(axassoc_type, type, axassoc: $o).
12.37/2.47	thf(hoaslamnotvar_type, type, hoaslamnotvar: $o).
12.37/2.47	thf(hoaslam_type, type, hoaslam: subst > (subst > term > term) > term).
12.37/2.47	thf(hoasinduction_lem2_lthm_type, type, hoasinduction_lem2_lthm: $o).
12.37/2.47	thf(pushprop_lem3v2_type, type, pushprop_lem3v2: $o).
12.37/2.47	thf(hoasinduction_lem3b_gthm_type, type, hoasinduction_lem3b_gthm: $o).
12.37/2.47	thf(pushprop_lem0_type, type, pushprop_lem0: $o).
12.37/2.47	thf(hoaslaminj_gthm_type, type, hoaslaminj_gthm: $o).
12.37/2.47	thf(hoasinduction_lem3_type, type, hoasinduction_lem3: $o).
12.37/2.47	thf(hoasinduction_lem2_type, type, hoasinduction_lem2: $o).
12.37/2.47	thf(hoasinduction_lem0_type, type, hoasinduction_lem0: $o).
12.37/2.47	thf(hoaslaminj_lthm_type, type, hoaslaminj_lthm: $o).
12.37/2.47	thf(hoasinduction_lem3aaa_type, type, hoasinduction_lem3aaa: $o).
12.37/2.47	thf(axidr_type, type, axidr: $o).
12.37/2.47	thf('#sk3_type', type, '#sk3': term).
12.37/2.47	thf(hoasapnotvar_lthm_type, type, hoasapnotvar_lthm: $o).
12.37/2.47	thf('#sk5_type', type, '#sk5': subst).
12.37/2.47	thf(hoasinduction_lem3v2_f_type, type, hoasinduction_lem3v2_f: $o).
12.37/2.47	thf(pushprop_lem2v2_gthm_type, type, pushprop_lem2v2_gthm: $o).
12.37/2.47	thf(substmonoid_lthm_type, type, substmonoid_lthm: $o).
12.37/2.47	thf(axabs_type, type, axabs: $o).
12.37/2.47	thf(hoasinduction_lem3v2_gthm_type, type, hoasinduction_lem3v2_gthm: $o).
12.37/2.47	thf(hoasvar_type, type, hoasvar: subst > term > subst > $o).
12.37/2.47	thf(hoasinduction_lem2v2_gthm_type, type, hoasinduction_lem2v2_gthm: $o).
12.37/2.47	thf(ulamvar1_type, type, ulamvar1: $o).
12.37/2.47	thf(hoasinduction_lem1v2_gthm_type, type, hoasinduction_lem1v2_gthm: $o).
12.37/2.47	thf(induction_type, type, induction: $o).
12.37/2.47	thf(pushprop_lem1v2_lthm_type, type, pushprop_lem1v2_lthm: $o).
12.37/2.47	thf(axscons_type, type, axscons: $o).
12.37/2.47	thf(pushprop_lem1_gthm_type, type, pushprop_lem1_gthm: $o).
12.37/2.47	thf(induction2lem_gthm_type, type, induction2lem_gthm: $o).
12.37/2.47	thf(pushprop_lem0_gthm_type, type, pushprop_lem0_gthm: $o).
12.37/2.47	thf(termmset_lthm_type, type, termmset_lthm: $o).
12.37/2.47	thf(d2subst_type, type, d2subst: d_subst > subst).
12.37/2.47	thf(hoasinduction_lthm_type, type, hoasinduction_lthm: $o).
12.37/2.47	thf(hoasinduction_no_psi_cond_type, type, hoasinduction_no_psi_cond: $o).
12.37/2.47	thf(axclos, conjecture,
12.37/2.47	  (( axclos ) <=>
12.37/2.47	   ( ![A:term,M:subst,N:subst]:
12.37/2.47	     ( ( sub @ ( sub @ A @ M ) @ N ) = ( sub @ A @ ( comp @ M @ N ) ) ) ))).
12.37/2.47	thf(zf_stmt_0, negated_conjecture,
12.37/2.47	  (~( ( axclos ) <=>
12.37/2.47	      ( ![A:term,M:subst,N:subst]:
12.37/2.47	        ( ( sub @ ( sub @ A @ M ) @ N ) = ( sub @ A @ ( comp @ M @ N ) ) ) ) )),
12.37/2.47	  inference('cnf.neg', [status(esa)], [axclos])).
12.37/2.47	thf(zip_derived_cl1, plain,
12.37/2.47	    (((axclos)
12.37/2.47	       != (((!!) @ (^[Y0 : term]:
12.37/2.47	                      (((!!) @ (^[Y1 : subst]:
12.37/2.47	                                  (((!!) @ (^[Y2 : subst]:
12.37/2.47	                                              (((sub @ (sub @ Y0 @ Y1) @ 
12.37/2.47	                                                Y2) = (sub @ Y0 @ 
12.37/2.47	                                                (comp @ Y1 @ Y2))))))))))))))),
12.37/2.47	    inference('cnf', [status(esa)], [zf_stmt_0])).
12.37/2.47	thf(alg444_1, axiom,
12.37/2.47	  (( ![T:term]: ( ?[DT:d_term]: ( ( T ) = ( d2term @ DT ) ) ) ) & 
12.37/2.47	   ( ![DT1:d_term,DT2:d_term]:
12.37/2.47	     ( ( ( d2term @ DT1 ) = ( d2term @ DT2 ) ) => ( ( DT1 ) = ( DT2 ) ) ) ) & 
12.37/2.47	   ( ![S:subst]: ( ?[DS:d_subst]: ( ( S ) = ( d2subst @ DS ) ) ) ) & 
12.37/2.47	   ( ![DS:d_subst]: ( ( DS ) = ( d_id ) ) ) & 
12.37/2.47	   ( ![DS1:d_subst,DS2:d_subst]:
12.37/2.47	     ( ( ( d2subst @ DS1 ) = ( d2subst @ DS2 ) ) => ( ( DS1 ) = ( DS2 ) ) ) ) & 
12.37/2.47	   ( ( ap @ ( d2term @ d_one ) @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 
12.37/2.47	   ( ( sub @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2term @ d_one ) ) & 
12.37/2.47	   ( ( id ) = ( d2subst @ d_id ) ) & 
12.37/2.47	   ( ( comp @ ( d2subst @ d_id ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 
12.37/2.47	   ( ( hoasap @
12.37/2.47	       ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) @ 
12.37/2.47	       ( d2term @ d_one ) ) =
12.37/2.47	     ( d2term @ d_one ) ) & 
12.37/2.47	   ( ( pushprop_p_and_p_prime ) =
12.37/2.47	     ( ^[A:term,M:subst,P:( term > $o ),Q:( term > $o )]:
12.37/2.47	       ( ![X:term]: ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) & 
12.37/2.47	   ( ( pushprop_lem1v2 ) <=>
12.37/2.47	     ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]:
12.37/2.47	       ( ( ~( P @ A ) ) | ( Q @ one ) | 
12.37/2.47	         ( ~( ![X:term]:
12.37/2.47	              ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( pushprop_lem1_gthm ) & ( axmap ) & 
12.37/2.47	   ( ( ![A:term,B:term]:
12.37/2.47	       ( ( ( sub @ A @ sh ) != ( sub @ B @ sh ) ) | ( ( A ) = ( B ) ) ) ) <=>
12.37/2.47	     ( shinj ) ) & 
12.37/2.47	   ( hoasinduction_lem1v2 ) & 
12.37/2.47	   ( ( ![A:term,B:term,C:term,D:term]:
12.37/2.47	       ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 
12.37/2.47	         ( ( C ) = ( D ) ) ) ) <=>
12.37/2.47	     ( hoasapinj2 ) ) & 
12.37/2.47	   ( ( induction2lem_lthm ) <=>
12.37/2.47	     ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) =>
12.37/2.47	       ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) =>
12.37/2.47	         ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) =>
12.37/2.47	           ( ( ![P:( term > $o ),Bound_variable_2140:term]:
12.37/2.47	               ( ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) | 
12.37/2.47	                 ( ~( ![A:term,B:term]:
12.37/2.47	                      ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | 
12.37/2.47	                        ( ~( P @ B ) ) ) ) ) | 
12.37/2.47	                 ( P @ Bound_variable_2140 ) | 
12.37/2.47	                 ( ~( ![A:term]: ( ( ~( P @ A ) ) | ( P @ ( lam @ A ) ) ) ) ) ) ) =>
12.37/2.47	             ( ![P:( term > $o ),Bound_variable_2340:term,
12.37/2.47	                 Bound_variable_2342:subst]:
12.37/2.47	               ( ( ~( ![A:term]:
12.37/2.47	                      ( ( ~( ![B:term]:
12.37/2.47	                             ( ( ~( P @ B ) ) | 
12.37/2.47	                               ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 
12.37/2.47	                        ( P @ ( lam @ A ) ) ) ) ) | 
12.37/2.47	                 ( ~( ![B:term]:
12.37/2.47	                      ( ( ~( var @ B ) ) | 
12.37/2.47	                        ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ) ) | 
12.37/2.47	                 ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 
12.37/2.47	                 ( ~( ![A:term,B:term]:
12.37/2.47	                      ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | 
12.37/2.47	                        ( ~( P @ A ) ) ) ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( apnotvar ) & ( pushprop_lthm_orig ) & 
12.37/2.47	   ( ( hoasinduction_no_psi_cond_lthm ) <=>
12.37/2.47	     ( ( ![P:( subst > term > subst > $o )]:
12.37/2.47	         ( ~( ![Q:( term > $o )]:
12.37/2.47	              ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) =>
12.37/2.47	       ( ( ![P:( term > $o ),Bound_variable_2367:term]:
12.37/2.47	           ( ( ~( ![A:term,B:term]:
12.37/2.47	                  ( ( ~( P @ A ) ) | ( ~( P @ B ) ) | ( P @ ( ap @ A @ B ) ) ) ) ) | 
12.37/2.47	             ( ~( ![A:term]:
12.37/2.47	                  ( ( P @ ( lam @ A ) ) | 
12.37/2.47	                    ( ~( ![B:term]:
12.37/2.47	                         ( ( ~( P @ B ) ) | 
12.37/2.47	                           ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) ) ) ) | 
12.37/2.47	             ( P @ Bound_variable_2367 ) | 
12.37/2.47	             ( ~( ![A:term]: ( ( P @ A ) | ( ~( var @ A ) ) ) ) ) ) ) =>
12.37/2.47	         ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.47	           ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ),
12.37/2.47	                 Bound_variable_2931:term]:
12.37/2.47	               ( ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 
12.37/2.47	                 ( Q @ ( lam @ Bound_variable_2931 ) ) | 
12.37/2.47	                 ( ~( ![B:term]:
12.37/2.47	                      ( ( ~( Q @ B ) ) | 
12.37/2.47	                        ( Q @
12.37/2.47	                          ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) | 
12.37/2.47	                 ( ~( ![F:( subst > term > term )]:
12.37/2.47	                      ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                             ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                               ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.47	                        ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.47	                        ( ~( ![A:term]:
12.37/2.47	                             ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.47	                               ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) ) ) ) ) ) =>
12.37/2.47	             ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]:
12.37/2.47	               ( ( P @ id @ Bound_variable_3295 @ id ) | 
12.37/2.47	                 ( ~( ![F:( subst > term > term )]:
12.37/2.47	                      ( ( ~( ![A:term]:
12.37/2.47	                             ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                               ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                        ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.47	                        ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                             ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                               ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.47	                 ( ~( ![A:term,B:term]:
12.37/2.47	                      ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.47	                        ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( ( ![P:( subst > term > subst > $o ),Bound_variable_3171:term]:
12.37/2.47	       ( ( ~( ![F:( subst > term > term ),Bound_variable_3149:term]:
12.37/2.47	              ( ( ~( ![A:term]:
12.37/2.47	                     ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                       ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                ( ~( ![Bound_variable_3072:subst,Bound_variable_3074:term,
12.37/2.47	                       Bound_variable_3076:subst]:
12.37/2.47	                     ( ( sub @
12.37/2.47	                         ( F @ Bound_variable_3072 @ Bound_variable_3074 ) @ 
12.37/2.47	                         Bound_variable_3076 ) =
12.37/2.47	                       ( sub @
12.37/2.47	                         ( sub @
12.37/2.47	                           Bound_variable_3149 @ 
12.37/2.47	                           ( push @ Bound_variable_3074 @ Bound_variable_3072 ) ) @ 
12.37/2.47	                         Bound_variable_3076 ) ) ) ) | 
12.37/2.47	                ( ~( ![Bound_variable_3090:subst,Bound_variable_3092:term,
12.37/2.47	                       Bound_variable_3094:subst]:
12.37/2.47	                     ( ( F @
12.37/2.47	                         ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) @ 
12.37/2.47	                         ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) ) =
12.37/2.47	                       ( sub @
12.37/2.47	                         Bound_variable_3149 @ 
12.37/2.47	                         ( push @
12.37/2.47	                           ( sub @ Bound_variable_3092 @ Bound_variable_3094 ) @ 
12.37/2.47	                           ( comp @ Bound_variable_3090 @ Bound_variable_3094 ) ) ) ) ) ) | 
12.37/2.47	                ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 
12.37/2.47	         ( P @
12.37/2.47	           id @ 
12.37/2.47	           ( lam @ ( sub @ Bound_variable_3171 @ ( push @ one @ sh ) ) ) @ id ) | 
12.37/2.47	         ( ~( ![B:term]:
12.37/2.47	              ( ( P @
12.37/2.47	                  id @ ( sub @ Bound_variable_3171 @ ( push @ B @ id ) ) @ id ) | 
12.37/2.47	                ( ~( P @ id @ B @ id ) ) ) ) ) ) ) <=>
12.37/2.47	     ( hoasinduction_lem3aaa ) ) & 
12.37/2.47	   ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]:
12.37/2.47	       ( ( P @
12.37/2.47	           id @ 
12.37/2.47	           ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 
12.37/2.47	         ( ~( ![B:term]:
12.37/2.47	              ( ( P @
12.37/2.47	                  id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 
12.37/2.47	                ( ~( P @ id @ B @ id ) ) ) ) ) | 
12.37/2.47	         ( ~( ![F:( subst > term > term )]:
12.37/2.47	              ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.47	                ( ~( ![A:term]:
12.37/2.47	                     ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                       ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) <=>
12.37/2.47	     ( hoasinduction_lem3aa_lthm ) ) & 
12.37/2.47	   ( ( termmset_lthm ) <=>
12.37/2.47	     ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.47	       ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) ) & 
12.37/2.47	   ( hoasinduction_lem1 ) & ( hoaslamnotap_lthm ) & 
12.37/2.47	   ( ( hoasinduction_lem0 ) <=>
12.37/2.47	     ( ![P:( subst > term > subst > $o )]:
12.37/2.47	       ( ~( ![Q:( term > $o )]:
12.37/2.47	            ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( ( hoasinduction ) <=>
12.37/2.47	     ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]:
12.37/2.47	       ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.47	              ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 
12.37/2.47	                ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 
12.37/2.47	         ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.47	              ( ( P @ M @ A @ ( comp @ K @ N ) ) | 
12.37/2.47	                ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 
12.37/2.47	         ( ~( ![A:term,B:term]:
12.37/2.47	              ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.47	                ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	         ( ~( ![F:( subst > term > term )]:
12.37/2.47	              ( ( ~( ![A:term]:
12.37/2.47	                     ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                       ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.47	                ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.47	         ( P @ id @ Bound_variable_3283 @ id ) | 
12.37/2.47	         ( ~( ![A:term]:
12.37/2.47	              ( ( P @ id @ A @ id ) | ( ~( var @ ( sub @ A @ id ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( hoasinduction_gthm ) & ( axapp ) & ( hoaslamnotvar_lthm ) & 
12.37/2.47	   ( ulamvarind ) & 
12.37/2.47	   ( ( induction ) <=>
12.37/2.47	     ( ![P:( term > $o ),Bound_variable_2140:term]:
12.37/2.47	       ( ( ~( ![A:term,B:term]:
12.37/2.47	              ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ) ) | 
12.37/2.47	         ( P @ Bound_variable_2140 ) | 
12.37/2.47	         ( ~( ![A:term]: ( ( P @ ( lam @ A ) ) | ( ~( P @ A ) ) ) ) ) | 
12.37/2.47	         ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) ) ) ) & 
12.37/2.47	   ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.47	       ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]:
12.37/2.47	           ( ( ~( ![F:( subst > term > term )]:
12.37/2.47	                  ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                         ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                           ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.47	                    ( ~( ![A:term]:
12.37/2.47	                         ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                           ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                    ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 
12.37/2.47	             ( P @
12.37/2.47	               id @ 
12.37/2.47	               ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ 
12.37/2.47	               id ) | 
12.37/2.47	             ( ~( ![B:term]:
12.37/2.47	                  ( ( ~( P @ id @ B @ id ) ) | 
12.37/2.47	                    ( P @
12.37/2.47	                      id @ 
12.37/2.47	                      ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) ) ) ) ) ) =>
12.37/2.47	         ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]:
12.37/2.47	           ( ( ~( ![B:term]:
12.37/2.47	                  ( ( ~( P @ id @ B @ id ) ) | 
12.37/2.47	                    ( P @
12.37/2.47	                      id @ 
12.37/2.47	                      ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) ) ) ) | 
12.37/2.47	             ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 
12.37/2.47	             ( ~( ![F:( subst > term > term )]:
12.37/2.47	                  ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.47	                    ( ~( ![A:term]:
12.37/2.47	                         ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                           ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                    ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                         ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                           ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) ) ) <=>
12.37/2.47	     ( hoasinduction_lem3a_lthm ) ) & 
12.37/2.47	   ( termmset_gthm ) & 
12.37/2.47	   ( ( hoasinduction_lem3aa ) <=>
12.37/2.47	     ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]:
12.37/2.47	       ( ( P @
12.37/2.47	           id @ 
12.37/2.47	           ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ id ) | 
12.37/2.47	         ( ~( ![B:term]:
12.37/2.47	              ( ( ~( P @ id @ B @ id ) ) | 
12.37/2.47	                ( P @
12.37/2.47	                  id @ ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) ) ) ) | 
12.37/2.47	         ( ~( ![F:( subst > term > term )]:
12.37/2.47	              ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.47	                ( ~( ![A:term]:
12.37/2.47	                     ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                       ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( hoaslamnotap_gthm ) & ( hoasinduction_lem3b_gthm ) & 
12.37/2.47	   ( pushprop_lem2v2 ) & ( hoasinduction_lem3a_gthm ) & ( axassoc ) & 
12.37/2.47	   ( pushprop_lthm ) & 
12.37/2.47	   ( ( ![A:term,B:term,C:term,D:term]:
12.37/2.47	       ( ( ( C ) = ( D ) ) | ( ( ap @ A @ C ) != ( ap @ B @ D ) ) ) ) <=>
12.37/2.47	     ( apinj2 ) ) & 
12.37/2.47	   ( ( ![A:term,B:term,C:term,D:term]:
12.37/2.47	       ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( A ) = ( B ) ) ) ) <=>
12.37/2.47	     ( apinj1 ) ) & 
12.37/2.47	   ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) <=>
12.37/2.47	     ( axvarcons ) ) & 
12.37/2.47	   ( hoasinduction_lem2v2_gthm ) & 
12.37/2.47	   ( ( pushprop_lem0 ) <=>
12.37/2.47	     ( ![P:( term > $o ),A:term,M:subst]:
12.37/2.47	       ( ~( ![Q:( term > $o )]:
12.37/2.47	            ( ~( ![X:term]:
12.37/2.47	                 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( ( hoasinduction_lem3v2a_lthm ) <=>
12.37/2.47	     ( ( ![B:term]:
12.37/2.47	         ( ~( ![F:( subst > term > term )]:
12.37/2.47	              ( ~( ![A:term,M:subst]:
12.37/2.47	                   ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) =>
12.37/2.47	       ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.47	         ( ![P:( subst > term > subst > $o ),Q:( term > $o ),
12.37/2.47	             Bound_variable_2931:term]:
12.37/2.47	           ( ( ~( ![F:( subst > term > term )]:
12.37/2.47	                  ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                         ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                           ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.47	                    ( ~( ![A:term]:
12.37/2.47	                         ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.47	                           ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.47	                    ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) | 
12.37/2.47	             ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 
12.37/2.47	             ( Q @ ( lam @ Bound_variable_2931 ) ) | 
12.37/2.47	             ( ~( ![B:term]:
12.37/2.47	                  ( ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) | 
12.37/2.47	                    ( ~( Q @ B ) ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( hoasinduction_lem1_lthm ) & 
12.37/2.47	   ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.47	       ( ( ![P:( term > $o ),Bound_variable_2340:term,
12.37/2.47	             Bound_variable_2342:subst]:
12.37/2.47	           ( ( ~( ![A:term,B:term]:
12.37/2.47	                  ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ) ) | 
12.37/2.47	             ( ~( ![A:term]:
12.37/2.47	                  ( ( ~( ![B:term]:
12.37/2.47	                         ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 
12.37/2.47	                           ( ~( P @ B ) ) ) ) ) | 
12.37/2.47	                    ( P @ ( lam @ A ) ) ) ) ) | 
12.37/2.47	             ( ~( ![B:term]:
12.37/2.47	                  ( ( P @ ( sub @ B @ Bound_variable_2342 ) ) | 
12.37/2.47	                    ( ~( var @ B ) ) ) ) ) | 
12.37/2.47	             ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) ) ) =>
12.37/2.47	         ( ![P:( term > $o ),Bound_variable_2367:term]:
12.37/2.47	           ( ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) | 
12.37/2.47	             ( ~( ![A:term]:
12.37/2.47	                  ( ( ~( ![B:term]:
12.37/2.47	                         ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 
12.37/2.47	                           ( ~( P @ B ) ) ) ) ) | 
12.37/2.47	                    ( P @ ( lam @ A ) ) ) ) ) | 
12.37/2.47	             ( P @ Bound_variable_2367 ) | 
12.37/2.47	             ( ~( ![A:term,B:term]:
12.37/2.47	                  ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ) ) ) ) ) ) <=>
12.37/2.47	     ( induction2_lthm ) ) & 
12.37/2.47	   ( pushprop ) & 
12.37/2.47	   ( ( hoasinduction_lem3a ) <=>
12.37/2.47	     ( ![P:( subst > term > subst > $o ),Bound_variable_3232:term]:
12.37/2.47	       ( ( ~( ![B:term]:
12.37/2.47	              ( ( ~( P @ id @ B @ id ) ) | 
12.37/2.47	                ( P @
12.37/2.47	                  id @ ( sub @ Bound_variable_3232 @ ( push @ B @ id ) ) @ id ) ) ) ) | 
12.37/2.47	         ( P @ id @ ( lam @ Bound_variable_3232 ) @ id ) | 
12.37/2.47	         ( ~( ![F:( subst > term > term )]:
12.37/2.47	              ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.47	                ( ~( ![A:term]:
12.37/2.47	                     ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.47	                       ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 
12.37/2.47	                ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) ) & 
12.37/2.47	   ( hoasinduction_lem1_gthm ) & 
12.37/2.47	   ( ( ![F:( subst > term > term ),Bound_variable_2603:term,
12.37/2.47	         Bound_variable_2605:term]:
12.37/2.47	       ( ( ( lam @ ( F @ sh @ one ) ) !=
12.37/2.47	           ( ap @ ( sub @ Bound_variable_2603 @ id ) @ Bound_variable_2605 ) ) | 
12.37/2.47	         ( ~( ![M:subst,A:term,N:subst]:
12.37/2.47	              ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.47	                ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) <=>
12.37/2.47	     ( hoaslamnotap ) ) & 
12.37/2.47	   ( ( induction2 ) <=>
12.37/2.47	     ( ![P:( term > $o ),Bound_variable_2367:term]:
12.37/2.47	       ( ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) | 
12.37/2.47	         ( ~( ![A:term,B:term]:
12.37/2.47	              ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ) ) | 
12.37/2.47	         ( ~( ![A:term]:
12.37/2.47	              ( ( ~( ![B:term]:
12.37/2.47	                     ( ( ~( P @ B ) ) | 
12.37/2.47	                       ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 
12.37/2.47	                ( P @ ( lam @ A ) ) ) ) ) | 
12.37/2.48	         ( P @ Bound_variable_2367 ) ) ) ) & 
12.37/2.48	   ( pushprop_lem3v2 ) & ( pushprop_lem2v2_gthm ) & 
12.37/2.48	   ( ( pushprop_lem1_lthm ) <=>
12.37/2.48	     ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) =>
12.37/2.48	       ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) =>
12.37/2.48	         ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]:
12.37/2.48	           ( ( K @ ( sub @ A @ ( push @ B @ M ) ) ) | ( ~( P @ A ) ) ) ) ) ) ) & 
12.37/2.48	   ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) <=>
12.37/2.48	     ( axshiftcons ) ) & 
12.37/2.48	   ( ( termmset ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 
12.37/2.48	   ( hoasapnotvar_lthm ) & 
12.37/2.48	   ( ( hoasinduction_lem3v2_lthm ) <=>
12.37/2.48	     ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.48	       ( ![P:( subst > term > subst > $o ),Q:( term > $o ),
12.37/2.48	           Bound_variable_2910:term]:
12.37/2.48	         ( ( ~( ![B:term]:
12.37/2.48	                ( ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) | 
12.37/2.48	                  ( ~( Q @ B ) ) ) ) ) | 
12.37/2.48	           ( Q @ ( lam @ Bound_variable_2910 ) ) | 
12.37/2.48	           ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 
12.37/2.48	           ( ~( ![F:( subst > term > term )]:
12.37/2.48	                ( ( ~( ![A:term]:
12.37/2.48	                       ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.48	                         ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	                  ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                  ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                       ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                         ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.48	           ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                  ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	           ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 
12.37/2.48	                  ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( ( ( ![P:( subst > term > subst > $o )]:
12.37/2.48	         ( ~( ![Q:( term > $o )]:
12.37/2.48	              ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) =>
12.37/2.48	       ( ( ![P:( term > $o ),Bound_variable_2367:term]:
12.37/2.48	           ( ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) | 
12.37/2.48	             ( ~( ![A:term,B:term]:
12.37/2.48	                  ( ( ~( P @ A ) ) | ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) ) ) ) | 
12.37/2.48	             ( P @ Bound_variable_2367 ) | 
12.37/2.48	             ( ~( ![A:term]:
12.37/2.48	                  ( ( ~( ![B:term]:
12.37/2.48	                         ( ( ~( P @ B ) ) | 
12.37/2.48	                           ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 
12.37/2.48	                    ( P @ ( lam @ A ) ) ) ) ) ) ) =>
12.37/2.48	         ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.48	           ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ),
12.37/2.48	                 Bound_variable_2931:term]:
12.37/2.48	               ( ( ~( ![B:term]:
12.37/2.48	                      ( ( ~( Q @ B ) ) | 
12.37/2.48	                        ( Q @
12.37/2.48	                          ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) | 
12.37/2.48	                 ( Q @ ( lam @ Bound_variable_2931 ) ) | 
12.37/2.48	                 ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 
12.37/2.48	                 ( ~( ![F:( subst > term > term )]:
12.37/2.48	                      ( ( ~( ![A:term]:
12.37/2.48	                             ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                               ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 
12.37/2.48	                        ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                        ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                             ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                               ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) =>
12.37/2.48	             ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]:
12.37/2.48	               ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                      ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                        ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	                 ( ~( ![A:term]:
12.37/2.48	                      ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ) ) | 
12.37/2.48	                 ( ~( ![A:term,B:term]:
12.37/2.48	                      ( ( ~( P @ id @ B @ id ) ) | 
12.37/2.48	                        ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.48	                        ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	                 ( P @ id @ Bound_variable_3283 @ id ) | 
12.37/2.48	                 ( ~( ![F:( subst > term > term )]:
12.37/2.48	                      ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                             ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                               ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.48	                        ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                        ( ~( ![A:term]:
12.37/2.48	                             ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                               ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) ) ) ) | 
12.37/2.48	                 ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                      ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 
12.37/2.48	                        ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) ) ) ) ) <=>
12.37/2.48	     ( hoasinduction_lthm_3 ) ) & 
12.37/2.48	   ( ( axvarid ) <=> ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) ) & 
12.37/2.48	   ( ( pushprop_lem0_lthm ) <=>
12.37/2.48	     ( ![P:( term > $o ),A:term,M:subst]:
12.37/2.48	       ( ~( ![Q:( term > $o )]:
12.37/2.48	            ( ~( ![X:term]:
12.37/2.48	                 ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( ( hoasinduction_lem3v2 ) <=>
12.37/2.48	     ( ![P:( subst > term > subst > $o ),Q:( term > $o ),
12.37/2.48	         Bound_variable_2910:term]:
12.37/2.48	       ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 
12.37/2.48	                ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 
12.37/2.48	         ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( P @ M @ A @ ( comp @ K @ N ) ) | 
12.37/2.48	                ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) | 
12.37/2.48	         ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 
12.37/2.48	         ( Q @ ( lam @ Bound_variable_2910 ) ) | 
12.37/2.48	         ( ~( ![B:term]:
12.37/2.48	              ( ( ~( Q @ B ) ) | 
12.37/2.48	                ( Q @ ( sub @ Bound_variable_2910 @ ( push @ B @ id ) ) ) ) ) ) | 
12.37/2.48	         ( ~( ![F:( subst > term > term )]:
12.37/2.48	              ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.48	                ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                ( ~( ![A:term]:
12.37/2.48	                     ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.48	                       ( ~( P @ id @ A @ id ) ) ) ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( ulamvarsh ) & ( substmonoid_gthm ) & 
12.37/2.48	   ( ~( hoasvar @
12.37/2.48	        ( d2subst @ d_id ) @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) ) & 
12.37/2.48	   ( pushprop_lem2v2_lthm ) & ( induction2_gthm ) & 
12.37/2.48	   ( ( ![P:( subst > term > subst > $o ),Bound_variable_3295:term]:
12.37/2.48	       ( ( ~( ![A:term,B:term]:
12.37/2.48	              ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.48	                ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	         ( ~( ![F:( subst > term > term )]:
12.37/2.48	              ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                ( ~( ![A:term]:
12.37/2.48	                     ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                       ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 
12.37/2.48	                ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.48	         ( P @ id @ Bound_variable_3295 @ id ) ) ) <=>
12.37/2.48	     ( hoasinduction_no_psi_cond ) ) & 
12.37/2.48	   ( lamnotvar ) & 
12.37/2.48	   ( ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) & 
12.37/2.48	       ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) ) <=>
12.37/2.48	     ( substmonoid ) ) & 
12.37/2.48	   ( ( ![B:term]:
12.37/2.48	       ( ~( ![F:( subst > term > term )]:
12.37/2.48	            ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) <=>
12.37/2.48	     ( hoasinduction_lem3b ) ) & 
12.37/2.48	   ( hoasinduction_lem2_gthm ) & ( hoasinduction_lem3_gthm ) & 
12.37/2.48	   ( ( ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) =>
12.37/2.48	       ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) =>
12.37/2.48	         ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) & 
12.37/2.48	           ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) ) ) ) <=>
12.37/2.48	     ( substmonoid_lthm ) ) & 
12.37/2.48	   ( ( hoasinduction_lem0_lthm ) <=>
12.37/2.48	     ( ![P:( subst > term > subst > $o )]:
12.37/2.48	       ( ~( ![Q:( term > $o )]:
12.37/2.48	            ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( hoaslaminj_gthm ) & 
12.37/2.48	   ( ( axidl ) <=> ( ![M:subst]: ( ( M ) = ( comp @ id @ M ) ) ) ) & 
12.37/2.48	   ( hoaslamnotvar ) & ( hoasapinj1_gthm ) & ( ~( lamnotap ) ) & 
12.37/2.48	   ( hoasapinj2_gthm ) & ( hoasinduction_lem2_lthm ) & ( axabs ) & 
12.37/2.48	   ( pushprop_gthm ) & 
12.37/2.48	   ( ( hoasinduction_lem3_lthm ) <=>
12.37/2.48	     ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.48	       ( ( ![P:( subst > term > subst > $o ),Bound_variable_3046:term]:
12.37/2.48	           ( ( ~( ![F:( subst > term > term )]:
12.37/2.48	                  ( ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                    ( ~( ![A:term]:
12.37/2.48	                         ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.48	                           ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	                    ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                         ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                           ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.48	             ( P @
12.37/2.48	               id @ 
12.37/2.48	               ( lam @ ( sub @ Bound_variable_3046 @ ( push @ one @ sh ) ) ) @ 
12.37/2.48	               id ) | 
12.37/2.48	             ( ~( ![B:term]:
12.37/2.48	                  ( ( P @
12.37/2.48	                      id @ 
12.37/2.48	                      ( sub @ Bound_variable_3046 @ ( push @ B @ id ) ) @ id ) | 
12.37/2.48	                    ( ~( P @ id @ B @ id ) ) ) ) ) ) ) =>
12.37/2.48	         ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]:
12.37/2.48	           ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                  ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 
12.37/2.48	                    ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 
12.37/2.48	             ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                  ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                    ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	             ( ~( ![F:( subst > term > term )]:
12.37/2.48	                  ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                         ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                           ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.48	                    ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                    ( ~( ![A:term]:
12.37/2.48	                         ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                           ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) ) ) ) | 
12.37/2.48	             ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 
12.37/2.48	             ( ~( ![B:term]:
12.37/2.48	                  ( ( ~( P @ id @ B @ id ) ) | 
12.37/2.48	                    ( P @
12.37/2.48	                      id @ 
12.37/2.48	                      ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( ( laminj ) <=>
12.37/2.48	     ( ![A:term,B:term]:
12.37/2.48	       ( ( ( lam @ A ) != ( lam @ B ) ) | ( ( A ) = ( B ) ) ) ) ) & 
12.37/2.48	   ( ( pushprop_lem1 ) <=>
12.37/2.48	     ( ![P:( term > $o ),K:( term > $o ),A:term,M:subst,B:term]:
12.37/2.48	       ( ( ~( P @ A ) ) | ( K @ ( sub @ A @ ( push @ B @ M ) ) ) ) ) ) & 
12.37/2.48	   ( ( ![M:subst]: ( ( M ) = ( comp @ M @ id ) ) ) <=> ( axidr ) ) & 
12.37/2.48	   ( ( ![M:subst]:
12.37/2.48	       ( ( M ) = ( push @ ( sub @ one @ M ) @ ( comp @ sh @ M ) ) ) ) <=>
12.37/2.48	     ( axscons ) ) & 
12.37/2.48	   ( ( hoaslaminj_lthm ) <=>
12.37/2.48	     ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) =>
12.37/2.48	       ( ( ![A:term,M:subst]: ( ( M ) = ( comp @ sh @ ( push @ A @ M ) ) ) ) =>
12.37/2.48	         ( ( ![A:term,B:term]:
12.37/2.48	             ( ( ( A ) = ( B ) ) | ( ( lam @ A ) != ( lam @ B ) ) ) ) =>
12.37/2.48	           ( ![F:( subst > term > term ),
12.37/2.48	               Bound_variable_2547:( subst > term > term ),
12.37/2.48	               Bound_variable_2549:subst,Bound_variable_2551:term]:
12.37/2.48	             ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                    ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) =
12.37/2.48	                      ( Bound_variable_2547 @
12.37/2.48	                        ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.48	               ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) =
12.37/2.48	                 ( Bound_variable_2547 @
12.37/2.48	                   Bound_variable_2549 @ Bound_variable_2551 ) ) | 
12.37/2.48	               ( ( lam @ ( F @ sh @ one ) ) !=
12.37/2.48	                 ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) | 
12.37/2.48	               ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                    ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                      ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( ( ( ![A:term]: ( ( A ) = ( sub @ A @ id ) ) ) =>
12.37/2.48	       ( ( ![A:term,B:term,C:term,D:term]:
12.37/2.48	           ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( A ) = ( B ) ) ) ) =>
12.37/2.48	         ( ![A:term,B:term,C:term,D:term]:
12.37/2.48	           ( ( ( A ) = ( B ) ) | 
12.37/2.48	             ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ) ) ) <=>
12.37/2.48	     ( hoasapinj1_lthm ) ) & 
12.37/2.48	   ( ( hoasinduction_lem3v2a ) <=>
12.37/2.48	     ( ![P:( subst > term > subst > $o ),Q:( term > $o ),
12.37/2.48	         Bound_variable_2931:term]:
12.37/2.48	       ( ( ~( ![F:( subst > term > term )]:
12.37/2.48	              ( ( ~( ![A:term]:
12.37/2.48	                     ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.48	                       ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	                ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.48	         ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 
12.37/2.48	         ( Q @ ( lam @ Bound_variable_2931 ) ) | 
12.37/2.48	         ( ~( ![B:term]:
12.37/2.48	              ( ( ~( Q @ B ) ) | 
12.37/2.48	                ( Q @ ( sub @ Bound_variable_2931 @ ( push @ B @ id ) ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( ( ( ![A:term,B:term,C:term,D:term]:
12.37/2.48	         ( ( ( ap @ A @ C ) != ( ap @ B @ D ) ) | ( ( C ) = ( D ) ) ) ) =>
12.37/2.48	       ( ![A:term,B:term,C:term,D:term]:
12.37/2.48	         ( ( ( C ) = ( D ) ) | 
12.37/2.48	           ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) ) ) ) <=>
12.37/2.48	     ( hoasapinj2_lthm ) ) & 
12.37/2.48	   ( ( ![P:( subst > term > subst > $o ),Q:( term > $o ),
12.37/2.48	         Bound_variable_2820:term,Bound_variable_2822:term]:
12.37/2.48	       ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	         ( ~( Q @ Bound_variable_2820 ) ) | 
12.37/2.48	         ( Q @ ( ap @ Bound_variable_2820 @ Bound_variable_2822 ) ) | 
12.37/2.48	         ( ~( Q @ Bound_variable_2822 ) ) | 
12.37/2.48	         ( ~( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) | 
12.37/2.48	         ( ~( ![A:term,B:term]:
12.37/2.48	              ( ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.48	                ( ~( P @ id @ B @ id ) ) | ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	         ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 
12.37/2.48	                ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) ) <=>
12.37/2.48	     ( hoasinduction_lem2v2 ) ) & 
12.37/2.48	   ( axclos ) & ( hoaslamnotvar_gthm ) & ( pushprop_lem1v2_gthm ) & 
12.37/2.48	   ( ( hoasinduction_lem3b_lthm ) <=>
12.37/2.48	     ( ![B:term]:
12.37/2.48	       ( ~( ![F:( subst > term > term )]:
12.37/2.48	            ( ( F @ sh @ one ) != ( sub @ B @ ( push @ one @ sh ) ) ) ) ) ) ) & 
12.37/2.48	   ( pushprop_lem3v2_lthm ) & ( hoasapnotvar ) & 
12.37/2.48	   ( ( ( ![A:term,M:subst]: ( ( A ) = ( sub @ one @ ( push @ A @ M ) ) ) ) =>
12.37/2.48	       ( ![P:( term > $o ),Q:( term > $o ),A:term,M:subst]:
12.37/2.48	         ( ( ~( P @ A ) ) | 
12.37/2.48	           ( ~( ![X:term]:
12.37/2.48	                ( ( Q @ X ) <=> ( P @ ( sub @ X @ ( push @ A @ M ) ) ) ) ) ) | 
12.37/2.48	           ( Q @ one ) ) ) ) <=>
12.37/2.48	     ( pushprop_lem1v2_lthm ) ) & 
12.37/2.48	   ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term,
12.37/2.48	         Bound_variable_3001:term]:
12.37/2.48	       ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 
12.37/2.48	                ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 
12.37/2.48	         ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	         ( ~( ![A:term,B:term]:
12.37/2.48	              ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.48	                ( ~( P @ id @ B @ id ) ) ) ) ) | 
12.37/2.48	         ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 
12.37/2.48	         ( P @ id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 
12.37/2.48	         ( ~( P @ id @ Bound_variable_3001 @ id ) ) ) ) <=>
12.37/2.48	     ( hoasinduction_lem2 ) ) & 
12.37/2.48	   ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]:
12.37/2.48	       ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 
12.37/2.48	                ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) | 
12.37/2.48	         ( ~( ![F:( subst > term > term )]:
12.37/2.48	              ( ( ~( ![A:term]:
12.37/2.48	                     ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                       ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 
12.37/2.48	                ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                     ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                       ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.48	         ( ~( ![B:term]:
12.37/2.48	              ( ( P @
12.37/2.48	                  id @ ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ id ) | 
12.37/2.48	                ( ~( P @ id @ B @ id ) ) ) ) ) | 
12.37/2.48	         ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 
12.37/2.48	         ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	              ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) ) <=>
12.37/2.48	     ( hoasinduction_lem3 ) ) & 
12.37/2.48	   ( induction2lem_gthm ) & 
12.37/2.48	   ( ( ![F:( subst > term > term ),
12.37/2.48	         Bound_variable_2547:( subst > term > term ),
12.37/2.48	         Bound_variable_2549:subst,Bound_variable_2551:term]:
12.37/2.48	       ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	              ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.48	         ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	              ( ( sub @ ( Bound_variable_2547 @ M @ A ) @ N ) =
12.37/2.48	                ( Bound_variable_2547 @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.48	         ( ( F @ Bound_variable_2549 @ Bound_variable_2551 ) =
12.37/2.48	           ( Bound_variable_2547 @ Bound_variable_2549 @ Bound_variable_2551 ) ) | 
12.37/2.48	         ( ( lam @ ( F @ sh @ one ) ) !=
12.37/2.48	           ( lam @ ( Bound_variable_2547 @ sh @ one ) ) ) ) ) <=>
12.37/2.48	     ( hoaslaminj ) ) & 
12.37/2.48	   ( ( ( ![P:( term > $o ),Bound_variable_2367:term]:
12.37/2.48	         ( ( ~( ![A:term]:
12.37/2.48	                ( ( P @ ( lam @ A ) ) | 
12.37/2.48	                  ( ~( ![B:term]:
12.37/2.48	                       ( ( P @ ( sub @ A @ ( push @ B @ id ) ) ) | 
12.37/2.48	                         ( ~( P @ B ) ) ) ) ) ) ) ) | 
12.37/2.48	           ( P @ Bound_variable_2367 ) | 
12.37/2.48	           ( ~( ![A:term,B:term]:
12.37/2.48	                ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ) ) | 
12.37/2.48	           ( ~( ![A:term]: ( ( ~( var @ A ) ) | ( P @ A ) ) ) ) ) ) =>
12.37/2.48	       ( ( ![P:( subst > term > subst > $o ),Bound_variable_2999:term,
12.37/2.48	             Bound_variable_3001:term]:
12.37/2.48	           ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                  ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                    ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	             ( ~( ![A:term,B:term]:
12.37/2.48	                  ( ( ~( P @ id @ B @ id ) ) | 
12.37/2.48	                    ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.48	                    ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	             ( ~( P @ id @ Bound_variable_2999 @ id ) ) | 
12.37/2.48	             ( ~( P @ id @ Bound_variable_3001 @ id ) ) | 
12.37/2.48	             ( P @
12.37/2.48	               id @ ( ap @ Bound_variable_2999 @ Bound_variable_3001 ) @ id ) | 
12.37/2.48	             ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                  ( ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) | 
12.37/2.48	                    ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) ) ) ) ) =>
12.37/2.48	         ( ( ![P:( subst > term > subst > $o ),Bound_variable_3211:term]:
12.37/2.48	             ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                    ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 
12.37/2.48	                      ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 
12.37/2.48	               ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                    ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                      ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	               ( ~( ![B:term]:
12.37/2.48	                    ( ( P @
12.37/2.48	                        id @ 
12.37/2.48	                        ( sub @ Bound_variable_3211 @ ( push @ B @ id ) ) @ 
12.37/2.48	                        id ) | 
12.37/2.48	                      ( ~( P @ id @ B @ id ) ) ) ) ) | 
12.37/2.48	               ( P @ id @ ( lam @ Bound_variable_3211 ) @ id ) | 
12.37/2.48	               ( ~( ![F:( subst > term > term )]:
12.37/2.48	                    ( ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                           ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                             ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) | 
12.37/2.48	                      ( ~( ![A:term]:
12.37/2.48	                           ( ( P @ id @ ( F @ id @ A ) @ id ) | 
12.37/2.48	                             ( ~( P @ id @ A @ id ) ) ) ) ) | 
12.37/2.48	                      ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) ) ) ) ) ) =>
12.37/2.48	           ( ![P:( subst > term > subst > $o ),Bound_variable_3283:term]:
12.37/2.48	             ( ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                    ( ( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) | 
12.37/2.48	                      ( ~( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) ) | 
12.37/2.48	               ( ~( ![M:subst,A:term,N:subst,K:subst]:
12.37/2.48	                    ( ( ~( P @ ( comp @ M @ K ) @ ( sub @ A @ K ) @ N ) ) | 
12.37/2.48	                      ( P @ M @ A @ ( comp @ K @ N ) ) ) ) ) | 
12.37/2.48	               ( ~( ![A:term,B:term]:
12.37/2.48	                    ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                      ( P @ id @ ( ap @ ( sub @ A @ id ) @ B ) @ id ) | 
12.37/2.48	                      ( ~( P @ id @ B @ id ) ) ) ) ) | 
12.37/2.48	               ( P @ id @ Bound_variable_3283 @ id ) | 
12.37/2.48	               ( ~( ![F:( subst > term > term )]:
12.37/2.48	                    ( ( ~( ![A:term]:
12.37/2.48	                           ( ( ~( P @ id @ A @ id ) ) | 
12.37/2.48	                             ( P @ id @ ( F @ id @ A ) @ id ) ) ) ) | 
12.37/2.48	                      ( P @ id @ ( lam @ ( F @ sh @ one ) ) @ id ) | 
12.37/2.48	                      ( ~( ![M:subst,A:term,N:subst]:
12.37/2.48	                           ( ( sub @ ( F @ M @ A ) @ N ) =
12.37/2.48	                             ( F @ ( comp @ M @ N ) @ ( sub @ A @ N ) ) ) ) ) ) ) ) | 
12.37/2.48	               ( ~( ![A:term]:
12.37/2.48	                    ( ( ~( var @ ( sub @ A @ id ) ) ) | ( P @ id @ A @ id ) ) ) ) ) ) ) ) ) <=>
12.37/2.48	     ( hoasinduction_lthm ) ) & 
12.37/2.48	   ( ( hoasinduction_lem3v2_f_lthm ) <=>
12.37/2.48	     ( ![B:term]:
12.37/2.48	       ( ~( ![F:( subst > term > term )]:
12.37/2.48	            ( ~( ![A:term,M:subst]:
12.37/2.48	                 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( hoasinduction_lem3v2_gthm ) & ( ~( ulamvar1 ) ) & 
12.37/2.48	   ( ( hoasapinj1 ) <=>
12.37/2.48	     ( ![A:term,B:term,C:term,D:term]:
12.37/2.48	       ( ( ( ap @ ( sub @ A @ id ) @ C ) != ( ap @ ( sub @ B @ id ) @ D ) ) | 
12.37/2.48	         ( ( A ) = ( B ) ) ) ) ) & 
12.37/2.48	   ( hoasapnotvar_gthm ) & ( axvarshift ) & 
12.37/2.48	   ( ( ![B:term]:
12.37/2.48	       ( ~( ![F:( subst > term > term )]:
12.37/2.48	            ( ~( ![A:term,M:subst]:
12.37/2.48	                 ( ( sub @ B @ ( push @ A @ M ) ) = ( F @ M @ A ) ) ) ) ) ) ) <=>
12.37/2.48	     ( hoasinduction_lem3v2_f ) ) & 
12.37/2.48	   ( ( induction2lem ) <=>
12.37/2.48	     ( ![P:( term > $o ),Bound_variable_2340:term,Bound_variable_2342:subst]:
12.37/2.48	       ( ( ~( ![A:term,B:term]:
12.37/2.48	              ( ( P @ ( ap @ A @ B ) ) | ( ~( P @ B ) ) | ( ~( P @ A ) ) ) ) ) | 
12.37/2.48	         ( P @ ( sub @ Bound_variable_2340 @ Bound_variable_2342 ) ) | 
12.37/2.48	         ( ~( ![B:term]:
12.37/2.48	              ( ( ~( var @ B ) ) | ( P @ ( sub @ B @ Bound_variable_2342 ) ) ) ) ) | 
12.37/2.48	         ( ~( ![A:term]:
12.37/2.48	              ( ( ~( ![B:term]:
12.37/2.48	                     ( ( ~( P @ B ) ) | 
12.37/2.48	                       ( P @ ( sub @ A @ ( push @ B @ id ) ) ) ) ) ) | 
12.37/2.48	                ( P @ ( lam @ A ) ) ) ) ) ) ) ) & 
12.37/2.48	   ( hoasinduction_lem1v2_gthm ) & ( pushprop_lem0_gthm ) & 
12.37/2.48	   ( ~( var @ ( d2term @ d_one ) ) ) & 
12.37/2.48	   ( ( hoasinduction_p_and_p_prime ) =
12.37/2.48	     ( ^[P:( subst > term > subst > $o ),Q:( term > $o )]:
12.37/2.48	       ( ![X:term]: ( ( Q @ X ) <=> ( P @ id @ X @ id ) ) ) ) ) & 
12.37/2.48	   ( ( hoaslam ) =
12.37/2.48	     ( ^[Bound_variable_4913:subst,
12.37/2.48	         Bound_variable_4915:( subst > term > term )]:
12.37/2.48	       ( d2term @ d_one ) ) ) & 
12.37/2.48	   ( ( push @ ( d2term @ d_one ) @ ( d2subst @ d_id ) ) = ( d2subst @ d_id ) ) & 
12.37/2.48	   ( ( sh ) = ( d2subst @ d_id ) ) & 
12.37/2.48	   ( ( lam @ ( d2term @ d_one ) ) = ( d2term @ d_one ) ) & 
12.37/2.48	   ( ( one ) = ( d2term @ d_one ) ) & 
12.37/2.48	   ( ![DT:d_term]: ( ( DT ) = ( d_one ) ) ))).
12.37/2.48	thf(zip_derived_cl0, plain,
12.37/2.48	    ( (((((!!) @ (^[Y0 : term]:
12.37/2.48	                    (((??) @ (^[Y1 : d_term]: (((Y0) = (d2term @ Y1))))))))) & 
12.37/2.48	        (((!!) @ (^[Y0 : d_term]:
12.37/2.48	                    (((!!) @ (^[Y1 : d_term]:
12.37/2.48	                                (((((d2term @ Y0) = (d2term @ Y1))) =>
12.37/2.48	                                  (((Y0) = (Y1))))))))))) & 
12.37/2.48	        (((!!) @ (^[Y0 : subst]:
12.37/2.48	                    (((??) @ (^[Y1 : d_subst]: (((Y0) = (d2subst @ Y1))))))))) & 
12.37/2.48	        (((!!) @ (^[Y0 : d_subst]: (((Y0) = (d_id)))))) & 
12.37/2.48	        (((!!) @ (^[Y0 : d_subst]:
12.37/2.48	                    (((!!) @ (^[Y1 : d_subst]:
12.37/2.48	                                (((((d2subst @ Y0) = (d2subst @ Y1))) =>
12.37/2.48	                                  (((Y0) = (Y1))))))))))) & 
12.37/2.48	        (((ap @ (d2term @ d_one) @ (d2term @ d_one)) = (d2term @ d_one))) & 
12.37/2.48	        (((sub @ (d2term @ d_one) @ (d2subst @ d_id)) = (d2term @ d_one))) & 
12.37/2.48	        (((id) = (d2subst @ d_id))) & 
12.37/2.48	        (((comp @ (d2subst @ d_id) @ (d2subst @ d_id)) = (d2subst @ d_id))) & 
12.37/2.48	        (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ 
12.37/2.48	          (d2term @ d_one)) = (d2term @ d_one))) & 
12.37/2.48	        (((pushprop_p_and_p_prime) =
12.37/2.48	          ((^[Y0 : term,Y1 : subst,Y2 : term > $o,Y3 : term > $o]:
12.37/2.48	              (((!!) @ (^[Y4 : term]:
12.37/2.48	                          (((Y3 @ Y4) <=> (Y2 @ 
12.37/2.48	                            (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))) & 
12.37/2.48	        (((pushprop_lem1v2) <=>
12.37/2.48	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.48	                      (((!!) @ (^[Y1 : term > $o]:
12.37/2.48	                                  (((!!) @ (^[Y2 : term]:
12.37/2.48	                                              (((!!) @ (^[Y3 : subst]:
12.37/2.48	                                                          (((((~) @ (Y0 @ Y2))) | 
12.37/2.48	                                                            (Y1 @ one) | 
12.37/2.48	                                                            (((~) @ (
12.37/2.48	                                                              ((!!) @ (
12.37/2.48	                                                               ^[Y4 : term]:
12.37/2.48	                                                                 (((Y1 @ 
12.37/2.48	                                                                   Y4) <=>
12.37/2.48	                                                                   (Y0 @ 
12.37/2.48	                                                                   (sub @ 
12.37/2.48	                                                                    Y4 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    push @ 
12.37/2.48	                                                                    Y2 @ Y3)))))))))))))))))))))))))) & 
12.37/2.48	        pushprop_lem1_gthm & axmap & 
12.37/2.48	        (((((!!) @ (^[Y0 : term]:
12.37/2.48	                      (((!!) @ (^[Y1 : term]:
12.37/2.48	                                  (((((sub @ Y0 @ sh) != (sub @ Y1 @ sh))) |
12.37/2.48	                                    (((Y0) = (Y1))))))))))) <=>
12.37/2.48	          (shinj))) & 
12.37/2.48	        hoasinduction_lem1v2 & 
12.37/2.48	        (((((!!) @ (^[Y0 : term]:
12.37/2.48	                      (((!!) @ (^[Y1 : term]:
12.37/2.48	                                  (((!!) @ (^[Y2 : term]:
12.37/2.48	                                              (((!!) @ (^[Y3 : term]:
12.37/2.48	                                                          (((((ap @ 
12.37/2.48	                                                              (sub @ Y0 @ id) @ 
12.37/2.48	                                                              Y2) != (ap @ 
12.37/2.48	                                                              (sub @ Y1 @ id) @ 
12.37/2.48	                                                              Y3))) |
12.37/2.48	                                                            (((Y2) = (Y3))))))))))))))))) <=>
12.37/2.48	          (hoasapinj2))) & 
12.37/2.48	        (((induction2lem_lthm) <=>
12.37/2.48	          (((((!!) @ (^[Y0 : term]:
12.37/2.48	                        (((!!) @ (^[Y1 : subst]:
12.37/2.48	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.48	            (((((!!) @ (^[Y0 : term]:
12.37/2.48	                          (((!!) @ (^[Y1 : subst]:
12.37/2.48	                                      (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.48	              (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) =>
12.37/2.48	                (((((!!) @ (^[Y0 : term > $o]:
12.37/2.48	                              (((!!) @ (^[Y1 : term]:
12.37/2.48	                                          (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                                (((Y0 @ Y2) |
12.37/2.48	                                                                  (((~) @ (
12.37/2.48	                                                                    var @ Y2)))))))))) | 
12.37/2.48	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                                (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ Y2))) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    ap @ 
12.37/2.48	                                                                    Y2 @ Y3)) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ Y3))))))))))))) | 
12.37/2.48	                                            (Y0 @ Y1) | 
12.37/2.48	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                                (((((~) @ (
12.37/2.48	                                                                    Y0 @ Y2))) |
12.37/2.48	                                                                  (Y0 @ 
12.37/2.48	                                                                  (lam @ Y2))))))))))))))))) =>
12.37/2.48	                  (((!!) @ (^[Y0 : term > $o]:
12.37/2.48	                              (((!!) @ (^[Y1 : term]:
12.37/2.48	                                          (((!!) @ (^[Y2 : subst]:
12.37/2.48	                                                      (((((~) @ (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ Y4))) |
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y3 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    push @ 
12.37/2.48	                                                                    Y4 @ id)))))))))) |
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    lam @ Y3))))))))) | 
12.37/2.48	                                                        (((~) @ (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    var @ Y3))) |
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y3 @ Y2))))))))) | 
12.37/2.48	                                                        (Y0 @ (sub @ Y1 @ Y2)) | 
12.37/2.48	                                                        (((~) @ (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    ap @ 
12.37/2.48	                                                                    Y3 @ Y4)) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ Y4))) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ Y3)))))))))))))))))))))))))))))))))) & 
12.37/2.48	        apnotvar & pushprop_lthm_orig & 
12.37/2.48	        (((hoasinduction_no_psi_cond_lthm) <=>
12.37/2.48	          (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.48	                        (((~) @ (((!!) @ (^[Y1 : term > $o]:
12.37/2.48	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                                (((Y1 @ 
12.37/2.48	                                                                  Y2) <=>
12.37/2.48	                                                                  (Y0 @ id @ 
12.37/2.48	                                                                  Y2 @ id)))))))))))))))) =>
12.37/2.48	            (((((!!) @ (^[Y0 : term > $o]:
12.37/2.48	                          (((!!) @ (^[Y1 : term]:
12.37/2.48	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                            (((!!) @ (
12.37/2.48	                                                              ^[Y3 : term]:
12.37/2.48	                                                                (((((~) @ (
12.37/2.48	                                                                    Y0 @ Y2))) | 
12.37/2.48	                                                                  (((~) @ (
12.37/2.48	                                                                    Y0 @ Y3))) | 
12.37/2.48	                                                                  (Y0 @ 
12.37/2.48	                                                                   (ap @ 
12.37/2.48	                                                                    Y2 @ Y3)))))))))))) | 
12.37/2.48	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                            (((Y0 @ 
12.37/2.48	                                                              (lam @ Y2)) |
12.37/2.48	                                                              (((~) @ (
12.37/2.48	                                                                ((!!) @ (
12.37/2.48	                                                                 ^[Y3 : term]:
12.37/2.48	                                                                   ((
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ Y3))) |
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    push @ 
12.37/2.48	                                                                    Y3 @ id))))))))))))))))) | 
12.37/2.48	                                        (Y0 @ Y1) | 
12.37/2.48	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                            (((Y0 @ Y2) |
12.37/2.48	                                                              (((~) @ (
12.37/2.48	                                                                var @ Y2)))))))))))))))))) =>
12.37/2.48	              (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.48	                (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.48	                              (((!!) @ (^[Y1 : term > $o]:
12.37/2.48	                                          (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                      (((((~) @ (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (Y1 @ 
12.37/2.48	                                                                    Y3) <=>
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    Y3 @ id)))))))) | 
12.37/2.48	                                                        (Y1 @ (lam @ Y2)) | 
12.37/2.48	                                                        (((~) @ (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y1 @ Y3))) |
12.37/2.48	                                                                    (Y1 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    push @ 
12.37/2.48	                                                                    Y3 @ id)))))))))) | 
12.37/2.48	                                                        (((~) @ (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : 
12.37/2.48	                                                                    subst > 
12.37/2.48	                                                                    term > term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y5 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y6 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (sub @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y3 @ 
12.37/2.48	                                                                    Y4 @ Y5) @ 
12.37/2.48	                                                                    Y6) =
12.37/2.48	                                                                    (Y3 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    comp @ 
12.37/2.48	                                                                    Y4 @ Y6) @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y5 @ Y6))))))))))))))) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    lam @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y3 @ 
12.37/2.48	                                                                    sh @ one)) @ 
12.37/2.48	                                                                    id) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    Y4 @ id))) |
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y3 @ 
12.37/2.48	                                                                    id @ Y4) @ 
12.37/2.48	                                                                    id)))))))))))))))))))))))))) =>
12.37/2.48	                  (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.48	                              (((!!) @ (^[Y1 : term]:
12.37/2.48	                                          (((Y0 @ id @ Y1 @ id) | 
12.37/2.48	                                            (((~) @ (((!!) @ (^[Y2 : 
12.37/2.48	                                                                subst > term > term]:
12.37/2.48	                                                                (((((~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y3 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    id @ Y3) @ 
12.37/2.48	                                                                    id) |
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    Y3 @ id)))))))))) | 
12.37/2.48	                                                                  (Y0 @ id @ 
12.37/2.48	                                                                   (lam @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    sh @ one)) @ 
12.37/2.48	                                                                   id) | 
12.37/2.48	                                                                  (((~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y3 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y5 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (sub @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    Y3 @ Y4) @ 
12.37/2.48	                                                                    Y5) =
12.37/2.48	                                                                    (Y2 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    comp @ 
12.37/2.48	                                                                    Y3 @ Y5) @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
12.37/2.48	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                                (((!!) @ (
12.37/2.48	                                                                  ^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    ap @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y2 @ id) @ 
12.37/2.48	                                                                    Y3) @ id) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    Y3 @ id))) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    Y2 @ id))))))))))))))))))))))))))))))) & 
12.37/2.48	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.48	                      (((!!) @ (^[Y1 : term]:
12.37/2.48	                                  (((((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.48	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    id @ Y4) @ 
12.37/2.48	                                                                    id) |
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    Y4 @ id)))))))))) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y5 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y6 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (sub @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    Y4 @ Y5) @ 
12.37/2.48	                                                                    Y6) =
12.37/2.48	                                                                    (sub @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y3 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    push @ 
12.37/2.48	                                                                    Y5 @ Y4)) @ 
12.37/2.48	                                                                    Y6)))))))))))))) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (~) @ (
12.37/2.48	                                                                    (
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y4 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y5 : term]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (!!) @ (
12.37/2.48	                                                                    ^[Y6 : subst]:
12.37/2.48	                                                                    ((
12.37/2.48	                                                                    (Y2 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    comp @ 
12.37/2.48	                                                                    Y4 @ Y6) @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y5 @ Y6)) =
12.37/2.48	                                                                    (sub @ 
12.37/2.48	                                                                    Y3 @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    push @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    sub @ 
12.37/2.48	                                                                    Y5 @ Y6) @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    comp @ 
12.37/2.48	                                                                    Y4 @ Y6)))))))))))))))) | 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y0 @ 
12.37/2.48	                                                                    id @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    lam @ 
12.37/2.48	                                                                    (
12.37/2.48	                                                                    Y2 @ 
12.37/2.48	                                                                    sh @ one)) @ 
12.37/2.48	                                                                    id))))))))))) | 
12.37/2.48	                                    (Y0 @ id @ 
12.37/2.48	                                     (lam @ (sub @ Y1 @ (push @ one @ sh))) @ 
12.37/2.48	                                     id) | 
12.37/2.48	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                        (((Y0 @ id @ 
12.37/2.48	                                                          (sub @ Y1 @ 
12.37/2.48	                                                           (push @ Y2 @ id)) @ 
12.37/2.48	                                                          id) |
12.37/2.48	                                                          (((~) @ (Y0 @ id @ 
12.37/2.48	                                                                   Y2 @ id)))))))))))))))))) <=>
12.37/2.48	          (hoasinduction_lem3aaa))) & 
12.37/2.48	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.48	                      (((!!) @ (^[Y1 : term]:
12.37/2.48	                                  (((Y0 @ id @ 
12.37/2.48	                                     (lam @ (sub @ Y1 @ (push @ one @ sh))) @ 
12.37/2.48	                                     id) | 
12.37/2.48	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.48	                                                        (((Y0 @ id @ 
12.37/2.48	                                                          (sub @ Y1 @ 
12.37/2.48	                                                           (push @ Y2 @ id)) @ 
12.37/2.49	                                                          id) |
12.37/2.49	                                                          (((~) @ (Y0 @ id @ 
12.37/2.49	                                                                   Y2 @ id)))))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.49	                                                        (((Y0 @ id @ 
12.37/2.49	                                                           (lam @ 
12.37/2.49	                                                            (Y2 @ sh @ one)) @ 
12.37/2.49	                                                           id) | 
12.37/2.49	                                                          (((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    id @ Y3) @ 
12.37/2.49	                                                                    id) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) | 
12.37/2.49	                                                          (((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))) <=>
12.37/2.49	          (hoasinduction_lem3aa_lthm))) & 
12.37/2.49	        (((termmset_lthm) <=>
12.37/2.49	          (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.49	            (((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))))))) & 
12.37/2.49	        hoasinduction_lem1 & hoaslamnotap_lthm & 
12.37/2.49	        (((hoasinduction_lem0) <=>
12.37/2.49	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                      (((~) @ (((!!) @ (^[Y1 : term > $o]:
12.37/2.49	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                              (((Y1 @ Y2) <=>
12.37/2.49	                                                                (Y0 @ id @ 
12.37/2.49	                                                                Y2 @ id)))))))))))))))))) & 
12.37/2.49	        (((hoasinduction) <=>
12.37/2.49	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.49	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y2 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    Y4) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y5 @ Y4)))))))))))))))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.49	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y5 @ Y4)) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y2 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    Y4))))))))))))))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    ap @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ id) @ 
12.37/2.49	                                                                    Y3) @ id) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id))) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y2 @ id))))))))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.49	                                                        (((((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    id @ Y3) @ 
12.37/2.49	                                                                    id) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) | 
12.37/2.49	                                                          (Y0 @ id @ 
12.37/2.49	                                                           (lam @ 
12.37/2.49	                                                            (Y2 @ sh @ one)) @ 
12.37/2.49	                                                           id) | 
12.37/2.49	                                                          (((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
12.37/2.49	                                    (Y0 @ id @ Y1 @ id) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((Y0 @ id @ Y2 @ 
12.37/2.49	                                                          id) |
12.37/2.49	                                                          (((~) @ (var @ 
12.37/2.49	                                                                   (sub @ 
12.37/2.49	                                                                    Y2 @ id))))))))))))))))))))) & 
12.37/2.49	        hoasinduction_gthm & axapp & hoaslamnotvar_lthm & ulamvarind & 
12.37/2.49	        (((induction) <=>
12.37/2.49	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y2))) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    ap @ 
12.37/2.49	                                                                    Y2 @ Y3)) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y3))))))))))))) | 
12.37/2.49	                                    (Y0 @ Y1) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((Y0 @ (lam @ Y2)) |
12.37/2.49	                                                          (((~) @ (Y0 @ Y2)))))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((((~) @ (var @ Y2))) |
12.37/2.49	                                                          (Y0 @ Y2)))))))))))))))))) & 
12.37/2.49	        (((((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.49	            (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                          (((!!) @ (^[Y1 : term]:
12.37/2.49	                                      (((((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.49	                                                            (((((~) @ (
12.37/2.49	                                                                ((!!) @ (
12.37/2.49	                                                                 ^[Y3 : subst]:
12.37/2.49	                                                                   ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5))))))))))))))) | 
12.37/2.49	                                                              (((~) @ (
12.37/2.49	                                                                ((!!) @ (
12.37/2.49	                                                                 ^[Y3 : term]:
12.37/2.49	                                                                   ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    id @ Y3) @ 
12.37/2.49	                                                                    id) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) | 
12.37/2.49	                                                              (Y0 @ id @ 
12.37/2.49	                                                               (lam @ 
12.37/2.49	                                                                (Y2 @ sh @ 
12.37/2.49	                                                                 one)) @ 
12.37/2.49	                                                               id)))))))) | 
12.37/2.49	                                        (Y0 @ id @ 
12.37/2.49	                                         (lam @ 
12.37/2.49	                                          (sub @ Y1 @ (push @ one @ sh))) @ 
12.37/2.49	                                         id) | 
12.37/2.49	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((((~) @ (
12.37/2.49	                                                                Y0 @ id @ 
12.37/2.49	                                                                Y2 @ id))) |
12.37/2.49	                                                              (Y0 @ id @ 
12.37/2.49	                                                              (sub @ Y1 @ 
12.37/2.49	                                                               (push @ Y2 @ 
12.37/2.49	                                                                id)) @ 
12.37/2.49	                                                              id)))))))))))))))) =>
12.37/2.49	              (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                          (((!!) @ (^[Y1 : term]:
12.37/2.49	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((((~) @ (
12.37/2.49	                                                                Y0 @ id @ 
12.37/2.49	                                                                Y2 @ id))) |
12.37/2.49	                                                              (Y0 @ id @ 
12.37/2.49	                                                              (sub @ Y1 @ 
12.37/2.49	                                                               (push @ Y2 @ 
12.37/2.49	                                                                id)) @ 
12.37/2.49	                                                              id)))))))) | 
12.37/2.49	                                        (Y0 @ id @ (lam @ Y1) @ id) | 
12.37/2.49	                                        (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.49	                                                            (((Y0 @ id @ 
12.37/2.49	                                                               (lam @ 
12.37/2.49	                                                                (Y2 @ sh @ 
12.37/2.49	                                                                 one)) @ 
12.37/2.49	                                                               id) | 
12.37/2.49	                                                              (((~) @ (
12.37/2.49	                                                                ((!!) @ (
12.37/2.49	                                                                 ^[Y3 : term]:
12.37/2.49	                                                                   ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    id @ Y3) @ 
12.37/2.49	                                                                    id) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) | 
12.37/2.49	                                                              (((~) @ (
12.37/2.49	                                                                ((!!) @ (
12.37/2.49	                                                                 ^[Y3 : subst]:
12.37/2.49	                                                                   ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))))))) <=>
12.37/2.49	          (hoasinduction_lem3a_lthm))) & 
12.37/2.49	        termmset_gthm & 
12.37/2.49	        (((hoasinduction_lem3aa) <=>
12.37/2.49	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((Y0 @ id @ 
12.37/2.49	                                     (lam @ (sub @ Y1 @ (push @ one @ sh))) @ 
12.37/2.49	                                     id) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((((~) @ (Y0 @ id @ 
12.37/2.49	                                                                   Y2 @ id))) |
12.37/2.49	                                                          (Y0 @ id @ 
12.37/2.49	                                                          (sub @ Y1 @ 
12.37/2.49	                                                           (push @ Y2 @ id)) @ 
12.37/2.49	                                                          id)))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.49	                                                        (((Y0 @ id @ 
12.37/2.49	                                                           (lam @ 
12.37/2.49	                                                            (Y2 @ sh @ one)) @ 
12.37/2.49	                                                           id) | 
12.37/2.49	                                                          (((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    id @ Y3) @ 
12.37/2.49	                                                                    id) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) | 
12.37/2.49	                                                          (((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))))) & 
12.37/2.49	        hoaslamnotap_gthm & hoasinduction_lem3b_gthm & pushprop_lem2v2 & 
12.37/2.49	        hoasinduction_lem3a_gthm & axassoc & pushprop_lthm & 
12.37/2.49	        (((((!!) @ (^[Y0 : term]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((!!) @ (^[Y2 : term]:
12.37/2.49	                                              (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                          (((((Y2) = (Y3))) |
12.37/2.49	                                                            (((ap @ Y0 @ 
12.37/2.49	                                                              Y2) != (ap @ 
12.37/2.49	                                                              Y1 @ Y3))))))))))))))))) <=>
12.37/2.49	          (apinj2))) & 
12.37/2.49	        (((((!!) @ (^[Y0 : term]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((!!) @ (^[Y2 : term]:
12.37/2.49	                                              (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                          (((((ap @ Y0 @ 
12.37/2.49	                                                              Y2) != (ap @ 
12.37/2.49	                                                              Y1 @ Y3))) |
12.37/2.49	                                                            (((Y0) = (Y1))))))))))))))))) <=>
12.37/2.49	          (apinj1))) & 
12.37/2.49	        (((((!!) @ (^[Y0 : term]:
12.37/2.49	                      (((!!) @ (^[Y1 : subst]:
12.37/2.49	                                  (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) <=>
12.37/2.49	          (axvarcons))) & 
12.37/2.49	        hoasinduction_lem2v2_gthm & 
12.37/2.49	        (((pushprop_lem0) <=>
12.37/2.49	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((!!) @ (^[Y2 : subst]:
12.37/2.49	                                              (((~) @ (((!!) @ (^[Y3 : term > $o]:
12.37/2.49	                                                                  (((~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y3 @ 
12.37/2.49	                                                                    Y4) <=>
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y1 @ Y2)))))))))))))))))))))))))) & 
12.37/2.49	        (((hoasinduction_lem3v2a_lthm) <=>
12.37/2.49	          (((((!!) @ (^[Y0 : term]:
12.37/2.49	                        (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
12.37/2.49	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                                (((!!) @ (
12.37/2.49	                                                                  ^[Y3 : subst]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y2 @ Y3)) =
12.37/2.49	                                                                    (Y1 @ 
12.37/2.49	                                                                    Y3 @ Y2))))))))))))))))))) =>
12.37/2.49	            (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.49	              (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                          (((!!) @ (^[Y1 : term > $o]:
12.37/2.49	                                      (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                  (((((~) @ (((!!) @ (
12.37/2.49	                                                              ^[Y3 : 
12.37/2.49	                                                                subst > term > term]:
12.37/2.49	                                                                (((((~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y6 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    Y4 @ Y5) @ 
12.37/2.49	                                                                    Y6) =
12.37/2.49	                                                                    (Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y4 @ Y6) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y5 @ Y6))))))))))))))) | 
12.37/2.49	                                                                  (((~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    id @ Y4) @ 
12.37/2.49	                                                                    id) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y4 @ id)))))))))) | 
12.37/2.49	                                                                  (Y0 @ id @ 
12.37/2.49	                                                                   (lam @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    sh @ one)) @ 
12.37/2.49	                                                                   id)))))))) | 
12.37/2.49	                                                    (((~) @ (((!!) @ (
12.37/2.49	                                                              ^[Y3 : term]:
12.37/2.49	                                                                (((Y1 @ 
12.37/2.49	                                                                  Y3) <=>
12.37/2.49	                                                                  (Y0 @ id @ 
12.37/2.49	                                                                  Y3 @ id)))))))) | 
12.37/2.49	                                                    (Y1 @ (lam @ Y2)) | 
12.37/2.49	                                                    (((~) @ (((!!) @ (
12.37/2.49	                                                              ^[Y3 : term]:
12.37/2.49	                                                                (((Y1 @ 
12.37/2.49	                                                                  (sub @ 
12.37/2.49	                                                                   Y2 @ 
12.37/2.49	                                                                   (push @ 
12.37/2.49	                                                                    Y3 @ id))) |
12.37/2.49	                                                                  (((~) @ (
12.37/2.49	                                                                    Y1 @ Y3))))))))))))))))))))))))))) & 
12.37/2.49	        hoasinduction_lem1_lthm & 
12.37/2.49	        (((((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.49	            (((((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                          (((!!) @ (^[Y1 : term]:
12.37/2.49	                                      (((!!) @ (^[Y2 : subst]:
12.37/2.49	                                                  (((((~) @ (((!!) @ (
12.37/2.49	                                                              ^[Y3 : term]:
12.37/2.49	                                                                (((!!) @ (
12.37/2.49	                                                                  ^[Y4 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y3))) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    ap @ 
12.37/2.49	                                                                    Y3 @ Y4)) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y4))))))))))))) | 
12.37/2.49	                                                    (((~) @ (((!!) @ (
12.37/2.49	                                                              ^[Y3 : term]:
12.37/2.49	                                                                (((((~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y4 @ id))) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y4)))))))))) |
12.37/2.49	                                                                  (Y0 @ 
12.37/2.49	                                                                  (lam @ Y3))))))))) | 
12.37/2.49	                                                    (((~) @ (((!!) @ (
12.37/2.49	                                                              ^[Y3 : term]:
12.37/2.49	                                                                (((Y0 @ 
12.37/2.49	                                                                  (sub @ 
12.37/2.49	                                                                   Y3 @ Y2)) |
12.37/2.49	                                                                  (((~) @ (
12.37/2.49	                                                                    var @ Y3)))))))))) | 
12.37/2.49	                                                    (Y0 @ (sub @ Y1 @ Y2))))))))))))) =>
12.37/2.49	              (((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                          (((!!) @ (^[Y1 : term]:
12.37/2.49	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((((~) @ (
12.37/2.49	                                                                var @ Y2))) |
12.37/2.49	                                                              (Y0 @ Y2)))))))) | 
12.37/2.49	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((((~) @ (
12.37/2.49	                                                                ((!!) @ (
12.37/2.49	                                                                 ^[Y3 : term]:
12.37/2.49	                                                                   ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y3 @ id))) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y3)))))))))) |
12.37/2.49	                                                              (Y0 @ 
12.37/2.49	                                                              (lam @ Y2))))))))) | 
12.37/2.49	                                        (Y0 @ Y1) | 
12.37/2.49	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((!!) @ (
12.37/2.49	                                                              ^[Y3 : term]:
12.37/2.49	                                                                (((((~) @ (
12.37/2.49	                                                                    Y0 @ Y2))) | 
12.37/2.49	                                                                  (Y0 @ 
12.37/2.49	                                                                   (ap @ 
12.37/2.49	                                                                    Y2 @ Y3)) | 
12.37/2.49	                                                                  (((~) @ (
12.37/2.49	                                                                    Y0 @ Y3))))))))))))))))))))))))) <=>
12.37/2.49	          (induction2_lthm))) & 
12.37/2.49	        pushprop & 
12.37/2.49	        (((hoasinduction_lem3a) <=>
12.37/2.49	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((((~) @ (Y0 @ id @ 
12.37/2.49	                                                                   Y2 @ id))) |
12.37/2.49	                                                          (Y0 @ id @ 
12.37/2.49	                                                          (sub @ Y1 @ 
12.37/2.49	                                                           (push @ Y2 @ id)) @ 
12.37/2.49	                                                          id)))))))) | 
12.37/2.49	                                    (Y0 @ id @ (lam @ Y1) @ id) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.49	                                                        (((Y0 @ id @ 
12.37/2.49	                                                           (lam @ 
12.37/2.49	                                                            (Y2 @ sh @ one)) @ 
12.37/2.49	                                                           id) | 
12.37/2.49	                                                          (((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    id @ Y3) @ 
12.37/2.49	                                                                    id)))))))) | 
12.37/2.49	                                                          (((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))))) & 
12.37/2.49	        hoasinduction_lem1_gthm & 
12.37/2.49	        (((((!!) @ (^[Y0 : subst > term > term]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((!!) @ (^[Y2 : term]:
12.37/2.49	                                              (((((lam @ (Y0 @ sh @ one)) !=
12.37/2.49	                                                  (ap @ (sub @ Y1 @ id) @ Y2))) |
12.37/2.49	                                                (((~) @ (((!!) @ (^[Y3 : subst]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5)))))))))))))))))))))))))) <=>
12.37/2.49	          (hoaslamnotap))) & 
12.37/2.49	        (((induction2) <=>
12.37/2.49	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.49	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((((~) @ (var @ Y2))) |
12.37/2.49	                                                          (Y0 @ Y2)))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    ap @ 
12.37/2.49	                                                                    Y2 @ Y3)) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y3))) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y2))))))))))))) | 
12.37/2.49	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                        (((((~) @ (((!!) @ (
12.37/2.49	                                                                    ^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y3))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) |
12.37/2.49	                                                          (Y0 @ (lam @ Y2))))))))) | 
12.37/2.49	                                    (Y0 @ Y1))))))))))) & 
12.37/2.49	        pushprop_lem3v2 & pushprop_lem2v2_gthm & 
12.37/2.49	        (((pushprop_lem1_lthm) <=>
12.37/2.49	          (((((!!) @ (^[Y0 : term]:
12.37/2.49	                        (((!!) @ (^[Y1 : subst]:
12.37/2.49	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.49	            (((((!!) @ (^[Y0 : term]:
12.37/2.49	                          (((!!) @ (^[Y1 : subst]:
12.37/2.49	                                      (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.49	              (((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                          (((!!) @ (^[Y1 : term > $o]:
12.37/2.49	                                      (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                  (((!!) @ (^[Y3 : subst]:
12.37/2.49	                                                              (((!!) @ (
12.37/2.49	                                                                ^[Y4 : term]:
12.37/2.49	                                                                  (((Y1 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y4 @ Y3))) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y2)))))))))))))))))))))))))) & 
12.37/2.49	        (((((!!) @ (^[Y0 : term]:
12.37/2.49	                      (((!!) @ (^[Y1 : subst]:
12.37/2.49	                                  (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) <=>
12.37/2.49	          (axshiftcons))) & 
12.37/2.49	        (((termmset) <=>
12.37/2.49	          (((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))))) & 
12.37/2.49	        hoasapnotvar_lthm & 
12.37/2.49	        (((hoasinduction_lem3v2_lthm) <=>
12.37/2.49	          (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.49	            (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                        (((!!) @ (^[Y1 : term > $o]:
12.37/2.49	                                    (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                (((((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y1 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y3 @ id))) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y1 @ Y3)))))))))) | 
12.37/2.49	                                                  (Y1 @ (lam @ Y2)) | 
12.37/2.49	                                                  (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y1 @ 
12.37/2.49	                                                                    Y3) <=>
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id)))))))) | 
12.37/2.49	                                                  (((~) @ (((!!) @ (^[Y3 : 
12.37/2.49	                                                                    subst > 
12.37/2.49	                                                                    term > term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    id @ Y4) @ 
12.37/2.49	                                                                    id) |
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y4 @ id)))))))))) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    lam @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    sh @ one)) @ 
12.37/2.49	                                                                    id) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y6 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    Y4 @ Y5) @ 
12.37/2.49	                                                                    Y6) =
12.37/2.49	                                                                    (Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y4 @ Y6) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y5 @ Y6)))))))))))))))))))))) | 
12.37/2.49	                                                  (((~) @ (((!!) @ (^[Y3 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y6 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y6) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y6) @ 
12.37/2.49	                                                                    Y5))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    Y4 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y6 @ Y5)))))))))))))))))) | 
12.37/2.49	                                                  (((~) @ (((!!) @ (^[Y3 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y6 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    Y4 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y6 @ Y5)))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y6) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y6) @ 
12.37/2.49	                                                                    Y5)))))))))))))))))))))))))))))))) & 
12.37/2.49	        (((((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                        (((~) @ (((!!) @ (^[Y1 : term > $o]:
12.37/2.49	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                                (((Y1 @ 
12.37/2.49	                                                                  Y2) <=>
12.37/2.49	                                                                  (Y0 @ id @ 
12.37/2.49	                                                                  Y2 @ id)))))))))))))))) =>
12.37/2.49	            (((((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                          (((!!) @ (^[Y1 : term]:
12.37/2.49	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((((~) @ (
12.37/2.49	                                                                var @ Y2))) |
12.37/2.49	                                                              (Y0 @ Y2)))))))) | 
12.37/2.49	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((!!) @ (
12.37/2.49	                                                              ^[Y3 : term]:
12.37/2.49	                                                                (((((~) @ (
12.37/2.49	                                                                    Y0 @ Y2))) | 
12.37/2.49	                                                                  (Y0 @ 
12.37/2.49	                                                                   (ap @ 
12.37/2.49	                                                                    Y2 @ Y3)) | 
12.37/2.49	                                                                  (((~) @ (
12.37/2.49	                                                                    Y0 @ Y3))))))))))))) | 
12.37/2.49	                                        (Y0 @ Y1) | 
12.37/2.49	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                            (((((~) @ (
12.37/2.49	                                                                ((!!) @ (
12.37/2.49	                                                                 ^[Y3 : term]:
12.37/2.49	                                                                   ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ Y3))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) |
12.37/2.49	                                                              (Y0 @ 
12.37/2.49	                                                              (lam @ Y2))))))))))))))))) =>
12.37/2.49	              (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.49	                (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                              (((!!) @ (^[Y1 : term > $o]:
12.37/2.49	                                          (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                      (((((~) @ (((!!) @ (
12.37/2.49	                                                                  ^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y1 @ Y3))) |
12.37/2.49	                                                                    (Y1 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    push @ 
12.37/2.49	                                                                    Y3 @ id)))))))))) | 
12.37/2.49	                                                        (Y1 @ (lam @ Y2)) | 
12.37/2.49	                                                        (((~) @ (((!!) @ (
12.37/2.49	                                                                  ^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (Y1 @ 
12.37/2.49	                                                                    Y3) <=>
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id)))))))) | 
12.37/2.49	                                                        (((~) @ (((!!) @ (
12.37/2.49	                                                                  ^[Y3 : 
12.37/2.49	                                                                    subst > 
12.37/2.49	                                                                    term > term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y4 @ id))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    id @ Y4) @ 
12.37/2.49	                                                                    id)))))))) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    lam @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    sh @ one)) @ 
12.37/2.49	                                                                    id) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y6 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    Y4 @ Y5) @ 
12.37/2.49	                                                                    Y6) =
12.37/2.49	                                                                    (Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y4 @ Y6) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y5 @ Y6))))))))))))))))))))))))))))))))) =>
12.37/2.49	                  (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.49	                              (((!!) @ (^[Y1 : term]:
12.37/2.49	                                          (((((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.49	                                                                (((!!) @ (
12.37/2.49	                                                                  ^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y2 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    Y4))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y5 @ Y4)))))))))))))))))) | 
12.37/2.49	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                                (((((~) @ (
12.37/2.49	                                                                    var @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ id)))) |
12.37/2.49	                                                                  (Y0 @ id @ 
12.37/2.49	                                                                  Y2 @ id)))))))) | 
12.37/2.49	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.49	                                                                (((!!) @ (
12.37/2.49	                                                                  ^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id))) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    ap @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y2 @ id) @ 
12.37/2.49	                                                                    Y3) @ id) | 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y2 @ id))))))))))))) | 
12.37/2.49	                                            (Y0 @ id @ Y1 @ id) | 
12.37/2.49	                                            (((~) @ (((!!) @ (^[Y2 : 
12.37/2.49	                                                                subst > term > term]:
12.37/2.49	                                                                (((((~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y3 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (sub @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ Y4) @ 
12.37/2.49	                                                                    Y5) =
12.37/2.49	                                                                    (Y2 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y4 @ Y5))))))))))))))) | 
12.37/2.49	                                                                  (Y0 @ id @ 
12.37/2.49	                                                                   (lam @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    sh @ one)) @ 
12.37/2.49	                                                                   id) | 
12.37/2.49	                                                                  (((~) @ (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y3 : term]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    Y3 @ id))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    id @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    id @ Y3) @ 
12.37/2.49	                                                                    id))))))))))))))) | 
12.37/2.49	                                            (((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.49	                                                                (((!!) @ (
12.37/2.49	                                                                  ^[Y3 : term]:
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y4 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (!!) @ (
12.37/2.49	                                                                    ^[Y5 : subst]:
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    ((
12.37/2.49	                                                                    (~) @ (
12.37/2.49	                                                                    Y0 @ 
12.37/2.49	                                                                    Y2 @ 
12.37/2.49	                                                                    Y3 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y5 @ Y4)))) |
12.37/2.49	                                                                    (Y0 @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    comp @ 
12.37/2.49	                                                                    Y2 @ Y5) @ 
12.37/2.49	                                                                    (
12.37/2.49	                                                                    sub @ 
12.37/2.49	                                                                    Y3 @ Y5) @ 
12.37/2.49	                                                                    Y4))))))))))))))))))))))))))))))))) <=>
12.37/2.49	          (hoasinduction_lthm_3))) & 
12.37/2.49	        (((axvarid) <=> (((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))))) & 
12.37/2.49	        (((pushprop_lem0_lthm) <=>
12.37/2.49	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.49	                      (((!!) @ (^[Y1 : term]:
12.37/2.50	                                  (((!!) @ (^[Y2 : subst]:
12.37/2.50	                                              (((~) @ (((!!) @ (^[Y3 : term > $o]:
12.37/2.50	                                                                  (((~) @ (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (Y3 @ 
12.37/2.50	                                                                    Y4) <=>
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    push @ 
12.37/2.50	                                                                    Y1 @ Y2)))))))))))))))))))))))))) & 
12.37/2.50	        (((hoasinduction_lem3v2) <=>
12.37/2.50	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                      (((!!) @ (^[Y1 : term > $o]:
12.37/2.50	                                  (((!!) @ (^[Y2 : term]:
12.37/2.50	                                              (((((~) @ (((!!) @ (^[Y3 : subst]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y6 @ Y5)))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    Y5))))))))))))))))) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : subst]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y6 @ Y5)) |
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    Y5))))))))))))))))))) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    Y3) <=>
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id)))))))) | 
12.37/2.50	                                                (Y1 @ (lam @ Y2)) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y1 @ Y3))) |
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    push @ 
12.37/2.50	                                                                    Y3 @ id)))))))))) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : 
12.37/2.50	                                                                    subst > 
12.37/2.50	                                                                    term > term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ Y5) @ 
12.37/2.50	                                                                    Y6) =
12.37/2.50	                                                                    (Y3 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y6))))))))))))))) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    lam @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    sh @ one)) @ 
12.37/2.50	                                                                    id) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    id @ Y4) @ 
12.37/2.50	                                                                    id) |
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y4 @ id)))))))))))))))))))))))))))))) & 
12.37/2.50	        ulamvarsh & substmonoid_gthm & 
12.37/2.50	        (((~) @ (hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ 
12.37/2.50	                 (d2subst @ d_id)))) & 
12.37/2.50	        pushprop_lem2v2_lthm & induction2_gthm & 
12.37/2.50	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                      (((!!) @ (^[Y1 : term]:
12.37/2.50	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    ap @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y2 @ id) @ 
12.37/2.50	                                                                    Y3) @ id) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id))) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y2 @ id))))))))))))) | 
12.37/2.50	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.50	                                                        (((Y0 @ id @ 
12.37/2.50	                                                           (lam @ 
12.37/2.50	                                                            (Y2 @ sh @ one)) @ 
12.37/2.50	                                                           id) | 
12.37/2.50	                                                          (((~) @ (((!!) @ (
12.37/2.50	                                                                    ^[Y3 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    id @ Y3) @ 
12.37/2.50	                                                                    id)))))))) | 
12.37/2.50	                                                          (((~) @ (((!!) @ (
12.37/2.50	                                                                    ^[Y3 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ Y4) @ 
12.37/2.50	                                                                    Y5) =
12.37/2.50	                                                                    (Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
12.37/2.50	                                    (Y0 @ id @ Y1 @ id))))))))) <=>
12.37/2.50	          (hoasinduction_no_psi_cond))) & 
12.37/2.50	        lamnotvar & 
12.37/2.50	        (((((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))) &
12.37/2.50	            (((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))))) <=>
12.37/2.50	          (substmonoid))) & 
12.37/2.50	        (((((!!) @ (^[Y0 : term]:
12.37/2.50	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
12.37/2.50	                                          (((Y1 @ sh @ one) != (sub @ Y0 @ 
12.37/2.50	                                            (push @ one @ sh)))))))))))) <=>
12.37/2.50	          (hoasinduction_lem3b))) & 
12.37/2.50	        hoasinduction_lem2_gthm & hoasinduction_lem3_gthm & 
12.37/2.50	        (((((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))) =>
12.37/2.50	            (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) =>
12.37/2.50	              (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) &
12.37/2.50	                (((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))))))))) <=>
12.37/2.50	          (substmonoid_lthm))) & 
12.37/2.50	        (((hoasinduction_lem0_lthm) <=>
12.37/2.50	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                      (((~) @ (((!!) @ (^[Y1 : term > $o]:
12.37/2.50	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                              (((Y1 @ Y2) <=>
12.37/2.50	                                                                (Y0 @ id @ 
12.37/2.50	                                                                Y2 @ id)))))))))))))))))) & 
12.37/2.50	        hoaslaminj_gthm & 
12.37/2.50	        (((axidl) <=> (((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))))) & 
12.37/2.50	        hoaslamnotvar & hoasapinj1_gthm & (((~) @ lamnotap)) & 
12.37/2.50	        hoasapinj2_gthm & hoasinduction_lem2_lthm & axabs & pushprop_gthm & 
12.37/2.50	        (((hoasinduction_lem3_lthm) <=>
12.37/2.50	          (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.50	            (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                          (((!!) @ (^[Y1 : term]:
12.37/2.50	                                      (((((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.50	                                                            (((Y0 @ id @ 
12.37/2.50	                                                               (lam @ 
12.37/2.50	                                                                (Y2 @ sh @ 
12.37/2.50	                                                                 one)) @ 
12.37/2.50	                                                               id) | 
12.37/2.50	                                                              (((~) @ (
12.37/2.50	                                                                ((!!) @ (
12.37/2.50	                                                                 ^[Y3 : term]:
12.37/2.50	                                                                   ((
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    id @ Y3) @ 
12.37/2.50	                                                                    id) |
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id)))))))))) | 
12.37/2.50	                                                              (((~) @ (
12.37/2.50	                                                                ((!!) @ (
12.37/2.50	                                                                 ^[Y3 : subst]:
12.37/2.50	                                                                   ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ Y4) @ 
12.37/2.50	                                                                    Y5) =
12.37/2.50	                                                                    (Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
12.37/2.50	                                        (Y0 @ id @ 
12.37/2.50	                                         (lam @ 
12.37/2.50	                                          (sub @ Y1 @ (push @ one @ sh))) @ 
12.37/2.50	                                         id) | 
12.37/2.50	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                            (((Y0 @ id @ 
12.37/2.50	                                                              (sub @ Y1 @ 
12.37/2.50	                                                               (push @ Y2 @ 
12.37/2.50	                                                                id)) @ 
12.37/2.50	                                                              id) |
12.37/2.50	                                                              (((~) @ (
12.37/2.50	                                                                Y0 @ id @ 
12.37/2.50	                                                                Y2 @ id)))))))))))))))))) =>
12.37/2.50	              (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                          (((!!) @ (^[Y1 : term]:
12.37/2.50	                                      (((((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.50	                                                            (((!!) @ (
12.37/2.50	                                                              ^[Y3 : term]:
12.37/2.50	                                                                (((!!) @ (
12.37/2.50	                                                                  ^[Y4 : subst]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y2 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    Y4) |
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y5 @ Y4)))))))))))))))))))) | 
12.37/2.50	                                        (((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.50	                                                            (((!!) @ (
12.37/2.50	                                                              ^[Y3 : term]:
12.37/2.50	                                                                (((!!) @ (
12.37/2.50	                                                                  ^[Y4 : subst]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y2 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    Y4))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y5 @ Y4)))))))))))))))))) | 
12.37/2.50	                                        (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.50	                                                            (((((~) @ (
12.37/2.50	                                                                ((!!) @ (
12.37/2.50	                                                                 ^[Y3 : subst]:
12.37/2.50	                                                                   ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ Y4) @ 
12.37/2.50	                                                                    Y5) =
12.37/2.50	                                                                    (Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y5))))))))))))))) | 
12.37/2.50	                                                              (Y0 @ id @ 
12.37/2.50	                                                               (lam @ 
12.37/2.50	                                                                (Y2 @ sh @ 
12.37/2.50	                                                                 one)) @ 
12.37/2.50	                                                               id) | 
12.37/2.50	                                                              (((~) @ (
12.37/2.50	                                                                ((!!) @ (
12.37/2.50	                                                                 ^[Y3 : term]:
12.37/2.50	                                                                   ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    id @ Y3) @ 
12.37/2.50	                                                                    id))))))))))))))) | 
12.37/2.50	                                        (Y0 @ id @ (lam @ Y1) @ id) | 
12.37/2.50	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                            (((((~) @ (
12.37/2.50	                                                                Y0 @ id @ 
12.37/2.50	                                                                Y2 @ id))) |
12.37/2.50	                                                              (Y0 @ id @ 
12.37/2.50	                                                              (sub @ Y1 @ 
12.37/2.50	                                                               (push @ Y2 @ 
12.37/2.50	                                                                id)) @ 
12.37/2.50	                                                              id)))))))))))))))))))))) & 
12.37/2.50	        (((laminj) <=>
12.37/2.50	          (((!!) @ (^[Y0 : term]:
12.37/2.50	                      (((!!) @ (^[Y1 : term]:
12.37/2.50	                                  (((((lam @ Y0) != (lam @ Y1))) |
12.37/2.50	                                    (((Y0) = (Y1))))))))))))) & 
12.37/2.50	        (((pushprop_lem1) <=>
12.37/2.50	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.50	                      (((!!) @ (^[Y1 : term > $o]:
12.37/2.50	                                  (((!!) @ (^[Y2 : term]:
12.37/2.50	                                              (((!!) @ (^[Y3 : subst]:
12.37/2.50	                                                          (((!!) @ (^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ Y2))) |
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    push @ 
12.37/2.50	                                                                    Y4 @ Y3)))))))))))))))))))))) & 
12.37/2.50	        (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) <=> (axidr))) & 
12.37/2.50	        (((((!!) @ (^[Y0 : subst]:
12.37/2.50	                      (((Y0) = (push @ (sub @ one @ Y0) @ (comp @ sh @ Y0))))))) <=>
12.37/2.50	          (axscons))) & 
12.37/2.50	        (((hoaslaminj_lthm) <=>
12.37/2.50	          (((((!!) @ (^[Y0 : term]:
12.37/2.50	                        (((!!) @ (^[Y1 : subst]:
12.37/2.50	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.50	            (((((!!) @ (^[Y0 : term]:
12.37/2.50	                          (((!!) @ (^[Y1 : subst]:
12.37/2.50	                                      (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.50	              (((((!!) @ (^[Y0 : term]:
12.37/2.50	                            (((!!) @ (^[Y1 : term]:
12.37/2.50	                                        (((((Y0) = (Y1))) |
12.37/2.50	                                          (((lam @ Y0) != (lam @ Y1))))))))))) =>
12.37/2.50	                (((!!) @ (^[Y0 : subst > term > term]:
12.37/2.50	                            (((!!) @ (^[Y1 : subst > term > term]:
12.37/2.50	                                        (((!!) @ (^[Y2 : subst]:
12.37/2.50	                                                    (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                (((((~) @ (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y1 @ 
12.37/2.50	                                                                    Y4 @ Y5) @ 
12.37/2.50	                                                                    Y6) =
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y6))))))))))))))) | 
12.37/2.50	                                                                  (((Y0 @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3) =
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    Y2 @ Y3))) | 
12.37/2.50	                                                                  (((lam @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    sh @ one)) !=
12.37/2.50	                                                                    (lam @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y1 @ 
12.37/2.50	                                                                    sh @ one)))) | 
12.37/2.50	                                                                  (((~) @ (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y4 @ Y5) @ 
12.37/2.50	                                                                    Y6) =
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y6))))))))))))))))))))))))))))))))))))) & 
12.37/2.50	        (((((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.50	            (((((!!) @ (^[Y0 : term]:
12.37/2.50	                          (((!!) @ (^[Y1 : term]:
12.37/2.50	                                      (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                  (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                              (((((ap @ Y0 @ 
12.37/2.50	                                                                  Y2) !=
12.37/2.50	                                                                  (ap @ Y1 @ 
12.37/2.50	                                                                  Y3))) |
12.37/2.50	                                                                (((Y0) = (Y1))))))))))))))))) =>
12.37/2.50	              (((!!) @ (^[Y0 : term]:
12.37/2.50	                          (((!!) @ (^[Y1 : term]:
12.37/2.50	                                      (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                  (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                              (((((Y0) = (Y1))) |
12.37/2.50	                                                                (((ap @ 
12.37/2.50	                                                                  (sub @ 
12.37/2.50	                                                                   Y0 @ id) @ 
12.37/2.50	                                                                  Y2) !=
12.37/2.50	                                                                  (ap @ 
12.37/2.50	                                                                  (sub @ 
12.37/2.50	                                                                   Y1 @ id) @ 
12.37/2.50	                                                                  Y3))))))))))))))))))))) <=>
12.37/2.50	          (hoasapinj1_lthm))) & 
12.37/2.50	        (((hoasinduction_lem3v2a) <=>
12.37/2.50	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                      (((!!) @ (^[Y1 : term > $o]:
12.37/2.50	                                  (((!!) @ (^[Y2 : term]:
12.37/2.50	                                              (((((~) @ (((!!) @ (^[Y3 : 
12.37/2.50	                                                                    subst > 
12.37/2.50	                                                                    term > term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    id @ Y4) @ 
12.37/2.50	                                                                    id) |
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y4 @ id)))))))))) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    lam @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    sh @ one)) @ 
12.37/2.50	                                                                    id) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ Y5) @ 
12.37/2.50	                                                                    Y6) =
12.37/2.50	                                                                    (Y3 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y6)))))))))))))))))))))) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    Y3) <=>
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id)))))))) | 
12.37/2.50	                                                (Y1 @ (lam @ Y2)) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y1 @ Y3))) |
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    push @ 
12.37/2.50	                                                                    Y3 @ id))))))))))))))))))))))) & 
12.37/2.50	        (((((((!!) @ (^[Y0 : term]:
12.37/2.50	                        (((!!) @ (^[Y1 : term]:
12.37/2.50	                                    (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                            (((((ap @ Y0 @ 
12.37/2.50	                                                                Y2) != (ap @ 
12.37/2.50	                                                                Y1 @ Y3))) |
12.37/2.50	                                                              (((Y2) = (Y3))))))))))))))))) =>
12.37/2.50	            (((!!) @ (^[Y0 : term]:
12.37/2.50	                        (((!!) @ (^[Y1 : term]:
12.37/2.50	                                    (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                            (((((Y2) = (Y3))) |
12.37/2.50	                                                              (((ap @ 
12.37/2.50	                                                                (sub @ Y0 @ 
12.37/2.50	                                                                 id) @ 
12.37/2.50	                                                                Y2) != (ap @ 
12.37/2.50	                                                                (sub @ Y1 @ 
12.37/2.50	                                                                 id) @ 
12.37/2.50	                                                                Y3))))))))))))))))))) <=>
12.37/2.50	          (hoasapinj2_lthm))) & 
12.37/2.50	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                      (((!!) @ (^[Y1 : term > $o]:
12.37/2.50	                                  (((!!) @ (^[Y2 : term]:
12.37/2.50	                                              (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                          (((((~) @ (
12.37/2.50	                                                              ((!!) @ (
12.37/2.50	                                                               ^[Y4 : subst]:
12.37/2.50	                                                                 (((!!) @ (
12.37/2.50	                                                                   ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y7 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y7) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y7) @ 
12.37/2.50	                                                                    Y6))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    Y5 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y7 @ Y6)))))))))))))))))) | 
12.37/2.50	                                                            (((~) @ (Y1 @ Y2))) | 
12.37/2.50	                                                            (Y1 @ 
12.37/2.50	                                                             (ap @ Y2 @ Y3)) | 
12.37/2.50	                                                            (((~) @ (Y1 @ Y3))) | 
12.37/2.50	                                                            (((~) @ (
12.37/2.50	                                                              ((!!) @ (
12.37/2.50	                                                               ^[Y4 : term]:
12.37/2.50	                                                                 (((Y1 @ 
12.37/2.50	                                                                   Y4) <=>
12.37/2.50	                                                                   (Y0 @ 
12.37/2.50	                                                                   id @ Y4 @ 
12.37/2.50	                                                                   id)))))))) | 
12.37/2.50	                                                            (((~) @ (
12.37/2.50	                                                              ((!!) @ (
12.37/2.50	                                                               ^[Y4 : term]:
12.37/2.50	                                                                 (((!!) @ (
12.37/2.50	                                                                   ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    ap @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ id) @ 
12.37/2.50	                                                                    Y5) @ id) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y5 @ id))) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y4 @ id))))))))))))) | 
12.37/2.50	                                                            (((~) @ (
12.37/2.50	                                                              ((!!) @ (
12.37/2.50	                                                               ^[Y4 : subst]:
12.37/2.50	                                                                 (((!!) @ (
12.37/2.50	                                                                   ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y7 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y7) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y7) @ 
12.37/2.50	                                                                    Y6) |
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    Y5 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y7 @ Y6)))))))))))))))))))))))))))))))))) <=>
12.37/2.50	          (hoasinduction_lem2v2))) & 
12.37/2.50	        axclos & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & 
12.37/2.50	        (((hoasinduction_lem3b_lthm) <=>
12.37/2.50	          (((!!) @ (^[Y0 : term]:
12.37/2.50	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
12.37/2.50	                                          (((Y1 @ sh @ one) != (sub @ Y0 @ 
12.37/2.50	                                            (push @ one @ sh)))))))))))))) & 
12.37/2.50	        pushprop_lem3v2_lthm & hoasapnotvar & 
12.37/2.50	        (((((((!!) @ (^[Y0 : term]:
12.37/2.50	                        (((!!) @ (^[Y1 : subst]:
12.37/2.50	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.50	            (((!!) @ (^[Y0 : term > $o]:
12.37/2.50	                        (((!!) @ (^[Y1 : term > $o]:
12.37/2.50	                                    (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                (((!!) @ (^[Y3 : subst]:
12.37/2.50	                                                            (((((~) @ (
12.37/2.50	                                                                Y0 @ Y2))) | 
12.37/2.50	                                                              (((~) @ (
12.37/2.50	                                                                ((!!) @ (
12.37/2.50	                                                                 ^[Y4 : term]:
12.37/2.50	                                                                   ((
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    Y4) <=>
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    push @ 
12.37/2.50	                                                                    Y2 @ Y3)))))))))) | 
12.37/2.50	                                                              (Y1 @ one))))))))))))))))) <=>
12.37/2.50	          (pushprop_lem1v2_lthm))) & 
12.37/2.50	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                      (((!!) @ (^[Y1 : term]:
12.37/2.50	                                  (((!!) @ (^[Y2 : term]:
12.37/2.50	                                              (((((~) @ (((!!) @ (^[Y3 : subst]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y6 @ Y5)))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    Y5))))))))))))))))) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : subst]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    Y5))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y6 @ Y5)))))))))))))))))) | 
12.37/2.50	                                                (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id))) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    ap @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y3 @ id) @ 
12.37/2.50	                                                                    Y4) @ id) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y4 @ id))))))))))))) | 
12.37/2.50	                                                (((~) @ (Y0 @ id @ Y1 @ id))) | 
12.37/2.50	                                                (Y0 @ id @ (ap @ Y1 @ Y2) @ 
12.37/2.50	                                                 id) | 
12.37/2.50	                                                (((~) @ (Y0 @ id @ Y2 @ id)))))))))))))) <=>
12.37/2.50	          (hoasinduction_lem2))) & 
12.37/2.50	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                      (((!!) @ (^[Y1 : term]:
12.37/2.50	                                  (((((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.50	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y5 @ Y4)))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y2 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    Y4))))))))))))))))) | 
12.37/2.50	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.50	                                                        (((((~) @ (((!!) @ (
12.37/2.50	                                                                    ^[Y3 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    id @ Y3) @ 
12.37/2.50	                                                                    id)))))))) | 
12.37/2.50	                                                          (Y0 @ id @ 
12.37/2.50	                                                           (lam @ 
12.37/2.50	                                                            (Y2 @ sh @ one)) @ 
12.37/2.50	                                                           id) | 
12.37/2.50	                                                          (((~) @ (((!!) @ (
12.37/2.50	                                                                    ^[Y3 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ Y4) @ 
12.37/2.50	                                                                    Y5) =
12.37/2.50	                                                                    (Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
12.37/2.50	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                        (((Y0 @ id @ 
12.37/2.50	                                                          (sub @ Y1 @ 
12.37/2.50	                                                           (push @ Y2 @ id)) @ 
12.37/2.50	                                                          id) |
12.37/2.50	                                                          (((~) @ (Y0 @ id @ 
12.37/2.50	                                                                   Y2 @ id)))))))))) | 
12.37/2.50	                                    (Y0 @ id @ (lam @ Y1) @ id) | 
12.37/2.50	                                    (((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.50	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y4 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y2 @ Y5) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y3 @ Y5) @ 
12.37/2.50	                                                                    Y4))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y5 @ Y4)))))))))))))))))))))))))) <=>
12.37/2.50	          (hoasinduction_lem3))) & 
12.37/2.50	        induction2lem_gthm & 
12.37/2.50	        (((((!!) @ (^[Y0 : subst > term > term]:
12.37/2.50	                      (((!!) @ (^[Y1 : subst > term > term]:
12.37/2.50	                                  (((!!) @ (^[Y2 : subst]:
12.37/2.50	                                              (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                          (((((~) @ (
12.37/2.50	                                                              ((!!) @ (
12.37/2.50	                                                               ^[Y4 : subst]:
12.37/2.50	                                                                 (((!!) @ (
12.37/2.50	                                                                   ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y4 @ Y5) @ 
12.37/2.50	                                                                    Y6) =
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y6))))))))))))))) | 
12.37/2.50	                                                            (((~) @ (
12.37/2.50	                                                              ((!!) @ (
12.37/2.50	                                                               ^[Y4 : subst]:
12.37/2.50	                                                                 (((!!) @ (
12.37/2.50	                                                                   ^[Y5 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (sub @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y1 @ 
12.37/2.50	                                                                    Y4 @ Y5) @ 
12.37/2.50	                                                                    Y6) =
12.37/2.50	                                                                    (Y1 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y5 @ Y6))))))))))))))) | 
12.37/2.50	                                                            (((Y0 @ Y2 @ 
12.37/2.50	                                                              Y3) = (Y1 @ 
12.37/2.50	                                                              Y2 @ Y3))) | 
12.37/2.50	                                                            (((lam @ 
12.37/2.50	                                                              (Y0 @ sh @ one)) !=
12.37/2.50	                                                              (lam @ 
12.37/2.50	                                                              (Y1 @ sh @ one)))))))))))))))))) <=>
12.37/2.50	          (hoaslaminj))) & 
12.37/2.50	        (((((((!!) @ (^[Y0 : term > $o]:
12.37/2.50	                        (((!!) @ (^[Y1 : term]:
12.37/2.50	                                    (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                          (((Y0 @ 
12.37/2.50	                                                            (lam @ Y2)) |
12.37/2.50	                                                            (((~) @ (
12.37/2.50	                                                              ((!!) @ (
12.37/2.50	                                                               ^[Y3 : term]:
12.37/2.50	                                                                 (((Y0 @ 
12.37/2.50	                                                                   (sub @ 
12.37/2.50	                                                                    Y2 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    push @ 
12.37/2.50	                                                                    Y3 @ id))) |
12.37/2.50	                                                                   ((
12.37/2.50	                                                                   (~) @ (
12.37/2.50	                                                                   Y0 @ Y3))))))))))))))))) | 
12.37/2.50	                                      (Y0 @ Y1) | 
12.37/2.50	                                      (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                          (((!!) @ (^[Y3 : term]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    ap @ 
12.37/2.50	                                                                    Y2 @ Y3)) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ Y3))) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ Y2))))))))))))) | 
12.37/2.50	                                      (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                          (((((~) @ (
12.37/2.50	                                                              var @ Y2))) |
12.37/2.50	                                                            (Y0 @ Y2)))))))))))))))) =>
12.37/2.50	            (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.50	                          (((!!) @ (^[Y1 : term]:
12.37/2.50	                                      (((!!) @ (^[Y2 : term]:
12.37/2.50	                                                  (((((~) @ (((!!) @ (
12.37/2.50	                                                              ^[Y3 : subst]:
12.37/2.50	                                                                (((!!) @ (
12.37/2.50	                                                                  ^[Y4 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y3 @ Y6) @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y4 @ Y6) @ 
12.37/2.50	                                                                    Y5))) |
12.37/2.50	                                                                    (Y0 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    comp @ 
12.37/2.50	                                                                    Y6 @ Y5)))))))))))))))))) | 
12.37/2.50	                                                    (((~) @ (((!!) @ (
12.37/2.50	                                                              ^[Y3 : term]:
12.37/2.50	                                                                (((!!) @ (
12.37/2.50	                                                                  ^[Y4 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y4 @ id))) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    ap @ 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    sub @ 
12.37/2.50	                                                                    Y3 @ id) @ 
12.37/2.50	                                                                    Y4) @ id) | 
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    id @ 
12.37/2.50	                                                                    Y3 @ id))))))))))))) | 
12.37/2.50	                                                    (((~) @ (Y0 @ id @ Y1 @ 
12.37/2.50	                                                             id))) | 
12.37/2.50	                                                    (((~) @ (Y0 @ id @ Y2 @ 
12.37/2.50	                                                             id))) | 
12.37/2.50	                                                    (Y0 @ id @ 
12.37/2.50	                                                     (ap @ Y1 @ Y2) @ id) | 
12.37/2.50	                                                    (((~) @ (((!!) @ (
12.37/2.50	                                                              ^[Y3 : subst]:
12.37/2.50	                                                                (((!!) @ (
12.37/2.50	                                                                  ^[Y4 : term]:
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y5 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (!!) @ (
12.37/2.50	                                                                    ^[Y6 : subst]:
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    ((
12.37/2.50	                                                                    (~) @ (
12.37/2.50	                                                                    Y0 @ 
12.37/2.50	                                                                    Y3 @ 
12.37/2.50	                                                                    Y4 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y6 @ Y5)))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y3 @ Y6) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y4 @ Y6) @ 
12.37/2.51	                                                                    Y5)))))))))))))))))))))))))))) =>
12.37/2.51	              (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                            (((!!) @ (^[Y1 : term]:
12.37/2.51	                                        (((((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.51	                                                              (((!!) @ (
12.37/2.51	                                                                ^[Y3 : term]:
12.37/2.51	                                                                  (((!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y2 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    Y4) |
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y5 @ Y4)))))))))))))))))))) | 
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.51	                                                              (((!!) @ (
12.37/2.51	                                                                ^[Y3 : term]:
12.37/2.51	                                                                  (((!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y2 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    Y4))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y5 @ Y4)))))))))))))))))) | 
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                              (((Y0 @ id @ 
12.37/2.51	                                                                (sub @ Y1 @ 
12.37/2.51	                                                                 (push @ 
12.37/2.51	                                                                  Y2 @ id)) @ 
12.37/2.51	                                                                id) |
12.37/2.51	                                                                (((~) @ (
12.37/2.51	                                                                  Y0 @ id @ 
12.37/2.51	                                                                  Y2 @ id)))))))))) | 
12.37/2.51	                                          (Y0 @ id @ (lam @ Y1) @ id) | 
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : subst > 
12.37/2.51	                                                                   term > term]:
12.37/2.51	                                                              (((((~) @ (
12.37/2.51	                                                                  ((!!) @ (
12.37/2.51	                                                                   ^[Y3 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ Y4) @ 
12.37/2.51	                                                                    Y5) =
12.37/2.51	                                                                    (Y2 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y4 @ Y5))))))))))))))) | 
12.37/2.51	                                                                (((~) @ (
12.37/2.51	                                                                  ((!!) @ (
12.37/2.51	                                                                   ^[Y3 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    id @ Y3) @ 
12.37/2.51	                                                                    id) |
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y3 @ id)))))))))) | 
12.37/2.51	                                                                (Y0 @ id @ 
12.37/2.51	                                                                 (lam @ 
12.37/2.51	                                                                  (Y2 @ sh @ 
12.37/2.51	                                                                   one)) @ 
12.37/2.51	                                                                 id)))))))))))))))) =>
12.37/2.51	                (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                            (((!!) @ (^[Y1 : term]:
12.37/2.51	                                        (((((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.51	                                                              (((!!) @ (
12.37/2.51	                                                                ^[Y3 : term]:
12.37/2.51	                                                                  (((!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y2 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    Y4) |
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y5 @ Y4)))))))))))))))))))) | 
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.51	                                                              (((!!) @ (
12.37/2.51	                                                                ^[Y3 : term]:
12.37/2.51	                                                                  (((!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y2 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    Y4))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y5 @ Y4)))))))))))))))))) | 
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                              (((!!) @ (
12.37/2.51	                                                                ^[Y3 : term]:
12.37/2.51	                                                                  (((
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y2 @ id))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ap @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y2 @ id) @ 
12.37/2.51	                                                                    Y3) @ id) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y3 @ id))))))))))))) | 
12.37/2.51	                                          (Y0 @ id @ Y1 @ id) | 
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : subst > 
12.37/2.51	                                                                   term > term]:
12.37/2.51	                                                              (((((~) @ (
12.37/2.51	                                                                  ((!!) @ (
12.37/2.51	                                                                   ^[Y3 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y3 @ id))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    id @ Y3) @ 
12.37/2.51	                                                                    id)))))))) | 
12.37/2.51	                                                                (Y0 @ id @ 
12.37/2.51	                                                                 (lam @ 
12.37/2.51	                                                                  (Y2 @ sh @ 
12.37/2.51	                                                                   one)) @ 
12.37/2.51	                                                                 id) | 
12.37/2.51	                                                                (((~) @ (
12.37/2.51	                                                                  ((!!) @ (
12.37/2.51	                                                                   ^[Y3 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ Y4) @ 
12.37/2.51	                                                                    Y5) =
12.37/2.51	                                                                    (Y2 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                              (((((~) @ (
12.37/2.51	                                                                  var @ 
12.37/2.51	                                                                  (sub @ 
12.37/2.51	                                                                   Y2 @ id)))) |
12.37/2.51	                                                                (Y0 @ id @ 
12.37/2.51	                                                                Y2 @ id)))))))))))))))))))))) <=>
12.37/2.51	          (hoasinduction_lthm))) & 
12.37/2.51	        (((hoasinduction_lem3v2_f_lthm) <=>
12.37/2.51	          (((!!) @ (^[Y0 : term]:
12.37/2.51	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                              (((!!) @ (
12.37/2.51	                                                                ^[Y3 : subst]:
12.37/2.51	                                                                  (((sub @ 
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y2 @ Y3)) =
12.37/2.51	                                                                    (Y1 @ 
12.37/2.51	                                                                    Y3 @ Y2))))))))))))))))))))) & 
12.37/2.51	        hoasinduction_lem3v2_gthm & (((~) @ ulamvar1)) & 
12.37/2.51	        (((hoasapinj1) <=>
12.37/2.51	          (((!!) @ (^[Y0 : term]:
12.37/2.51	                      (((!!) @ (^[Y1 : term]:
12.37/2.51	                                  (((!!) @ (^[Y2 : term]:
12.37/2.51	                                              (((!!) @ (^[Y3 : term]:
12.37/2.51	                                                          (((((ap @ 
12.37/2.51	                                                              (sub @ Y0 @ id) @ 
12.37/2.51	                                                              Y2) != (ap @ 
12.37/2.51	                                                              (sub @ Y1 @ id) @ 
12.37/2.51	                                                              Y3))) |
12.37/2.51	                                                            (((Y0) = (Y1))))))))))))))))))) & 
12.37/2.51	        hoasapnotvar_gthm & axvarshift & 
12.37/2.51	        (((((!!) @ (^[Y0 : term]:
12.37/2.51	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                              (((!!) @ (
12.37/2.51	                                                                ^[Y3 : subst]:
12.37/2.51	                                                                  (((sub @ 
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y2 @ Y3)) =
12.37/2.51	                                                                    (Y1 @ 
12.37/2.51	                                                                    Y3 @ Y2))))))))))))))))))) <=>
12.37/2.51	          (hoasinduction_lem3v2_f))) & 
12.37/2.51	        (((induction2lem) <=>
12.37/2.51	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.51	                      (((!!) @ (^[Y1 : term]:
12.37/2.51	                                  (((!!) @ (^[Y2 : subst]:
12.37/2.51	                                              (((((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ap @ 
12.37/2.51	                                                                    Y3 @ Y4)) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y4))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y3))))))))))))) | 
12.37/2.51	                                                (Y0 @ (sub @ Y1 @ Y2)) | 
12.37/2.51	                                                (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    var @ Y3))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ Y2))))))))) | 
12.37/2.51	                                                (((~) @ (((!!) @ (^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y4))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y4 @ id)))))))))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    lam @ Y3)))))))))))))))))))))) & 
12.37/2.51	        hoasinduction_lem1v2_gthm & pushprop_lem0_gthm & 
12.37/2.51	        (((~) @ (var @ (d2term @ d_one)))) & 
12.37/2.51	        (((hoasinduction_p_and_p_prime) =
12.37/2.51	          ((^[Y0 : subst > term > subst > $o,Y1 : term > $o]:
12.37/2.51	              (((!!) @ (^[Y2 : term]: (((Y1 @ Y2) <=> (Y0 @ id @ Y2 @ id)))))))))) & 
12.37/2.51	        (((hoaslam) =
12.37/2.51	          ((^[Y0 : subst,Y1 : subst > term > term]: (d2term @ d_one))))) & 
12.37/2.51	        (((push @ (d2term @ d_one) @ (d2subst @ d_id)) = (d2subst @ d_id))) & 
12.37/2.51	        (((sh) = (d2subst @ d_id))) & 
12.37/2.51	        (((lam @ (d2term @ d_one)) = (d2term @ d_one))) & 
12.37/2.51	        (((one) = (d2term @ d_one))) & 
12.37/2.51	        (((!!) @ (^[Y0 : d_term]: (((Y0) = (d_one))))))))),
12.37/2.51	    inference('cnf', [status(esa)], [alg444_1])).
12.37/2.51	thf(zip_derived_cl2, plain,
12.37/2.51	    ( (((((!!) @ (^[Y0 : term]:
12.37/2.51	                    (((??) @ (^[Y1 : d_term]: (((Y0) = (d2term @ Y1))))))))) & 
12.37/2.51	        (((!!) @ (^[Y0 : d_term]:
12.37/2.51	                    (((!!) @ (^[Y1 : d_term]:
12.37/2.51	                                (((((d2term @ Y0) = (d2term @ Y1))) =>
12.37/2.51	                                  (((Y0) = (Y1))))))))))) & 
12.37/2.51	        (((!!) @ (^[Y0 : subst]:
12.37/2.51	                    (((??) @ (^[Y1 : d_subst]: (((Y0) = (d2subst @ Y1))))))))) & 
12.37/2.51	        (((!!) @ (^[Y0 : d_subst]: (((Y0) = (d_id)))))) & 
12.37/2.51	        (((!!) @ (^[Y0 : d_subst]:
12.37/2.51	                    (((!!) @ (^[Y1 : d_subst]:
12.37/2.51	                                (((((d2subst @ Y0) = (d2subst @ Y1))) =>
12.37/2.51	                                  (((Y0) = (Y1))))))))))) & 
12.37/2.51	        (((ap @ (d2term @ d_one) @ (d2term @ d_one)) = (d2term @ d_one))) & 
12.37/2.51	        (((sub @ (d2term @ d_one) @ (d2subst @ d_id)) = (d2term @ d_one))) & 
12.37/2.51	        (((id) = (d2subst @ d_id))) & 
12.37/2.51	        (((comp @ (d2subst @ d_id) @ (d2subst @ d_id)) = (d2subst @ d_id))) & 
12.37/2.51	        (((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ 
12.37/2.51	          (d2term @ d_one)) = (d2term @ d_one))) & 
12.37/2.51	        (((pushprop_p_and_p_prime) =
12.37/2.51	          ((^[Y0 : term,Y1 : subst,Y2 : term > $o,Y3 : term > $o]:
12.37/2.51	              (((!!) @ (^[Y4 : term]:
12.37/2.51	                          (((Y3 @ Y4) <=> (Y2 @ 
12.37/2.51	                            (sub @ Y4 @ (push @ Y0 @ Y1)))))))))))) & 
12.37/2.51	        (((pushprop_lem1v2) <=>
12.37/2.51	          (((!!) @ (^[Y0 : term > $o]:
12.37/2.51	                      (((!!) @ (^[Y1 : term > $o]:
12.37/2.51	                                  (((!!) @ (^[Y2 : term]:
12.37/2.51	                                              (((!!) @ (^[Y3 : subst]:
12.37/2.51	                                                          (((((~) @ (Y0 @ Y2))) | 
12.37/2.51	                                                            (Y1 @ one) | 
12.37/2.51	                                                            (((~) @ (
12.37/2.51	                                                              ((!!) @ (
12.37/2.51	                                                               ^[Y4 : term]:
12.37/2.51	                                                                 (((Y1 @ 
12.37/2.51	                                                                   Y4) <=>
12.37/2.51	                                                                   (Y0 @ 
12.37/2.51	                                                                   (sub @ 
12.37/2.51	                                                                    Y4 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y2 @ Y3)))))))))))))))))))))))))) & 
12.37/2.51	        pushprop_lem1_gthm & axmap & 
12.37/2.51	        (((((!!) @ (^[Y0 : term]:
12.37/2.51	                      (((!!) @ (^[Y1 : term]:
12.37/2.51	                                  (((((sub @ Y0 @ sh) != (sub @ Y1 @ sh))) |
12.37/2.51	                                    (((Y0) = (Y1))))))))))) <=>
12.37/2.51	          (shinj))) & 
12.37/2.51	        hoasinduction_lem1v2 & 
12.37/2.51	        (((((!!) @ (^[Y0 : term]:
12.37/2.51	                      (((!!) @ (^[Y1 : term]:
12.37/2.51	                                  (((!!) @ (^[Y2 : term]:
12.37/2.51	                                              (((!!) @ (^[Y3 : term]:
12.37/2.51	                                                          (((((ap @ 
12.37/2.51	                                                              (sub @ Y0 @ id) @ 
12.37/2.51	                                                              Y2) != (ap @ 
12.37/2.51	                                                              (sub @ Y1 @ id) @ 
12.37/2.51	                                                              Y3))) |
12.37/2.51	                                                            (((Y2) = (Y3))))))))))))))))) <=>
12.37/2.51	          (hoasapinj2))) & 
12.37/2.51	        (((induction2lem_lthm) <=>
12.37/2.51	          (((((!!) @ (^[Y0 : term]:
12.37/2.51	                        (((!!) @ (^[Y1 : subst]:
12.37/2.51	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.51	            (((((!!) @ (^[Y0 : term]:
12.37/2.51	                          (((!!) @ (^[Y1 : subst]:
12.37/2.51	                                      (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) =>
12.37/2.51	              (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) =>
12.37/2.51	                (((((!!) @ (^[Y0 : term > $o]:
12.37/2.51	                              (((!!) @ (^[Y1 : term]:
12.37/2.51	                                          (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                                (((Y0 @ Y2) |
12.37/2.51	                                                                  (((~) @ (
12.37/2.51	                                                                    var @ Y2)))))))))) | 
12.37/2.51	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                                (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y2))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ap @ 
12.37/2.51	                                                                    Y2 @ Y3)) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y3))))))))))))) | 
12.37/2.51	                                            (Y0 @ Y1) | 
12.37/2.51	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                                (((((~) @ (
12.37/2.51	                                                                    Y0 @ Y2))) |
12.37/2.51	                                                                  (Y0 @ 
12.37/2.51	                                                                  (lam @ Y2))))))))))))))))) =>
12.37/2.51	                  (((!!) @ (^[Y0 : term > $o]:
12.37/2.51	                              (((!!) @ (^[Y1 : term]:
12.37/2.51	                                          (((!!) @ (^[Y2 : subst]:
12.37/2.51	                                                      (((((~) @ (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y4))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y4 @ id)))))))))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    lam @ Y3))))))))) | 
12.37/2.51	                                                        (((~) @ (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    var @ Y3))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ Y2))))))))) | 
12.37/2.51	                                                        (Y0 @ (sub @ Y1 @ Y2)) | 
12.37/2.51	                                                        (((~) @ (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ap @ 
12.37/2.51	                                                                    Y3 @ Y4)) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y4))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y3)))))))))))))))))))))))))))))))))) & 
12.37/2.51	        apnotvar & pushprop_lthm_orig & 
12.37/2.51	        (((hoasinduction_no_psi_cond_lthm) <=>
12.37/2.51	          (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                        (((~) @ (((!!) @ (^[Y1 : term > $o]:
12.37/2.51	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                                (((Y1 @ 
12.37/2.51	                                                                  Y2) <=>
12.37/2.51	                                                                  (Y0 @ id @ 
12.37/2.51	                                                                  Y2 @ id)))))))))))))))) =>
12.37/2.51	            (((((!!) @ (^[Y0 : term > $o]:
12.37/2.51	                          (((!!) @ (^[Y1 : term]:
12.37/2.51	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                            (((!!) @ (
12.37/2.51	                                                              ^[Y3 : term]:
12.37/2.51	                                                                (((((~) @ (
12.37/2.51	                                                                    Y0 @ Y2))) | 
12.37/2.51	                                                                  (((~) @ (
12.37/2.51	                                                                    Y0 @ Y3))) | 
12.37/2.51	                                                                  (Y0 @ 
12.37/2.51	                                                                   (ap @ 
12.37/2.51	                                                                    Y2 @ Y3)))))))))))) | 
12.37/2.51	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                            (((Y0 @ 
12.37/2.51	                                                              (lam @ Y2)) |
12.37/2.51	                                                              (((~) @ (
12.37/2.51	                                                                ((!!) @ (
12.37/2.51	                                                                 ^[Y3 : term]:
12.37/2.51	                                                                   ((
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ Y3))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y3 @ id))))))))))))))))) | 
12.37/2.51	                                        (Y0 @ Y1) | 
12.37/2.51	                                        (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                            (((Y0 @ Y2) |
12.37/2.51	                                                              (((~) @ (
12.37/2.51	                                                                var @ Y2)))))))))))))))))) =>
12.37/2.51	              (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
12.37/2.51	                (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                              (((!!) @ (^[Y1 : term > $o]:
12.37/2.51	                                          (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                      (((((~) @ (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (Y1 @ 
12.37/2.51	                                                                    Y3) <=>
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y3 @ id)))))))) | 
12.37/2.51	                                                        (Y1 @ (lam @ Y2)) | 
12.37/2.51	                                                        (((~) @ (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y1 @ Y3))) |
12.37/2.51	                                                                    (Y1 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y3 @ id)))))))))) | 
12.37/2.51	                                                        (((~) @ (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : 
12.37/2.51	                                                                    subst > 
12.37/2.51	                                                                    term > term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y6 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    Y4 @ Y5) @ 
12.37/2.51	                                                                    Y6) =
12.37/2.51	                                                                    (Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y4 @ Y6) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y5 @ Y6))))))))))))))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    lam @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    sh @ one)) @ 
12.37/2.51	                                                                    id) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y4 @ id))) |
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    id @ Y4) @ 
12.37/2.51	                                                                    id)))))))))))))))))))))))))) =>
12.37/2.51	                  (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                              (((!!) @ (^[Y1 : term]:
12.37/2.51	                                          (((Y0 @ id @ Y1 @ id) | 
12.37/2.51	                                            (((~) @ (((!!) @ (^[Y2 : 
12.37/2.51	                                                                subst > term > term]:
12.37/2.51	                                                                (((((~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y3 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    id @ Y3) @ 
12.37/2.51	                                                                    id) |
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y3 @ id)))))))))) | 
12.37/2.51	                                                                  (Y0 @ id @ 
12.37/2.51	                                                                   (lam @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    sh @ one)) @ 
12.37/2.51	                                                                   id) | 
12.37/2.51	                                                                  (((~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y3 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ Y4) @ 
12.37/2.51	                                                                    Y5) =
12.37/2.51	                                                                    (Y2 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
12.37/2.51	                                            (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                                (((!!) @ (
12.37/2.51	                                                                  ^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    ap @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y2 @ id) @ 
12.37/2.51	                                                                    Y3) @ id) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y3 @ id))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y2 @ id))))))))))))))))))))))))))))))) & 
12.37/2.51	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                      (((!!) @ (^[Y1 : term]:
12.37/2.51	                                  (((((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.51	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    id @ Y4) @ 
12.37/2.51	                                                                    id) |
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y4 @ id)))))))))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y6 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y4 @ Y5) @ 
12.37/2.51	                                                                    Y6) =
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    Y5 @ Y4)) @ 
12.37/2.51	                                                                    Y6)))))))))))))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y6 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (Y2 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y4 @ Y6) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y5 @ Y6)) =
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    Y3 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    push @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y5 @ Y6) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y4 @ Y6)))))))))))))))) | 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    lam @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    sh @ one)) @ 
12.37/2.51	                                                                    id))))))))))) | 
12.37/2.51	                                    (Y0 @ id @ 
12.37/2.51	                                     (lam @ (sub @ Y1 @ (push @ one @ sh))) @ 
12.37/2.51	                                     id) | 
12.37/2.51	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                        (((Y0 @ id @ 
12.37/2.51	                                                          (sub @ Y1 @ 
12.37/2.51	                                                           (push @ Y2 @ id)) @ 
12.37/2.51	                                                          id) |
12.37/2.51	                                                          (((~) @ (Y0 @ id @ 
12.37/2.51	                                                                   Y2 @ id)))))))))))))))))) <=>
12.37/2.51	          (hoasinduction_lem3aaa))) & 
12.37/2.51	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                      (((!!) @ (^[Y1 : term]:
12.37/2.51	                                  (((Y0 @ id @ 
12.37/2.51	                                     (lam @ (sub @ Y1 @ (push @ one @ sh))) @ 
12.37/2.51	                                     id) | 
12.37/2.51	                                    (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                        (((Y0 @ id @ 
12.37/2.51	                                                          (sub @ Y1 @ 
12.37/2.51	                                                           (push @ Y2 @ id)) @ 
12.37/2.51	                                                          id) |
12.37/2.51	                                                          (((~) @ (Y0 @ id @ 
12.37/2.51	                                                                   Y2 @ id)))))))))) | 
12.37/2.51	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
12.37/2.51	                                                        (((Y0 @ id @ 
12.37/2.51	                                                           (lam @ 
12.37/2.51	                                                            (Y2 @ sh @ one)) @ 
12.37/2.51	                                                           id) | 
12.37/2.51	                                                          (((~) @ (((!!) @ (
12.37/2.51	                                                                    ^[Y3 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    id @ Y3) @ 
12.37/2.51	                                                                    id) |
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (~) @ (
12.37/2.51	                                                                    Y0 @ 
12.37/2.51	                                                                    id @ 
12.37/2.51	                                                                    Y3 @ id)))))))))) | 
12.37/2.51	                                                          (((~) @ (((!!) @ (
12.37/2.51	                                                                    ^[Y3 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : term]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y5 : subst]:
12.37/2.51	                                                                    ((
12.37/2.51	                                                                    (sub @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    Y2 @ 
12.37/2.51	                                                                    Y3 @ Y4) @ 
12.37/2.51	                                                                    Y5) =
12.37/2.51	                                                                    (Y2 @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    comp @ 
12.37/2.51	                                                                    Y3 @ Y5) @ 
12.37/2.51	                                                                    (
12.37/2.51	                                                                    sub @ 
12.37/2.51	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))) <=>
12.37/2.51	          (hoasinduction_lem3aa_lthm))) & 
12.37/2.51	        termmset_lthm & hoasinduction_lem1 & hoaslamnotap_lthm & 
12.37/2.51	        (((hoasinduction_lem0) <=>
12.37/2.51	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                      (((~) @ (((!!) @ (^[Y1 : term > $o]:
12.37/2.51	                                          (((~) @ (((!!) @ (^[Y2 : term]:
12.37/2.51	                                                              (((Y1 @ Y2) <=>
12.37/2.51	                                                                (Y0 @ id @ 
12.37/2.51	                                                                Y2 @ id)))))))))))))))))) & 
12.37/2.51	        (((hoasinduction) <=>
12.37/2.51	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
12.37/2.51	                      (((!!) @ (^[Y1 : term]:
12.37/2.51	                                  (((((~) @ (((!!) @ (^[Y2 : subst]:
12.37/2.51	                                                        (((!!) @ (^[Y3 : term]:
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (
12.37/2.51	                                                                    (!!) @ (
12.37/2.51	                                                                    ^[Y4 : subst]:
12.37/2.51	                                                                    ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y5 : subst]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (Y0 @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    comp @ 
13.13/2.51	                                                                    Y2 @ Y5) @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    sub @ 
13.13/2.51	                                                                    Y3 @ Y5) @ 
13.13/2.51	                                                                    Y4) |
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    Y2 @ 
13.13/2.51	                                                                    Y3 @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    comp @ 
13.13/2.51	                                                                    Y5 @ Y4)))))))))))))))))))) | 
13.13/2.51	                                    (((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.51	                                                        (((!!) @ (^[Y3 : term]:
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y4 : subst]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y5 : subst]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (Y0 @ 
13.13/2.51	                                                                    Y2 @ 
13.13/2.51	                                                                    Y3 @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    comp @ 
13.13/2.51	                                                                    Y5 @ Y4)) |
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    comp @ 
13.13/2.51	                                                                    Y2 @ Y5) @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    sub @ 
13.13/2.51	                                                                    Y3 @ Y5) @ 
13.13/2.51	                                                                    Y4))))))))))))))))))) | 
13.13/2.51	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.51	                                                        (((!!) @ (^[Y3 : term]:
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    ap @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    sub @ 
13.13/2.51	                                                                    Y2 @ id) @ 
13.13/2.51	                                                                    Y3) @ id) | 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    Y3 @ id))) | 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    Y2 @ id))))))))))))) | 
13.13/2.51	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.51	                                                        (((((~) @ (((!!) @ (
13.13/2.51	                                                                    ^[Y3 : term]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    Y2 @ 
13.13/2.51	                                                                    id @ Y3) @ 
13.13/2.51	                                                                    id) |
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    Y3 @ id)))))))))) | 
13.13/2.51	                                                          (Y0 @ id @ 
13.13/2.51	                                                           (lam @ 
13.13/2.51	                                                            (Y2 @ sh @ one)) @ 
13.13/2.51	                                                           id) | 
13.13/2.51	                                                          (((~) @ (((!!) @ (
13.13/2.51	                                                                    ^[Y3 : subst]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y4 : term]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y5 : subst]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (sub @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    Y2 @ 
13.13/2.51	                                                                    Y3 @ Y4) @ 
13.13/2.51	                                                                    Y5) =
13.13/2.51	                                                                    (Y2 @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    comp @ 
13.13/2.51	                                                                    Y3 @ Y5) @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    sub @ 
13.13/2.51	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
13.13/2.51	                                    (Y0 @ id @ Y1 @ id) | 
13.13/2.51	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.51	                                                        (((Y0 @ id @ Y2 @ 
13.13/2.51	                                                          id) |
13.13/2.51	                                                          (((~) @ (var @ 
13.13/2.51	                                                                   (sub @ 
13.13/2.51	                                                                    Y2 @ id))))))))))))))))))))) & 
13.13/2.51	        hoasinduction_gthm & axapp & hoaslamnotvar_lthm & ulamvarind & 
13.13/2.51	        (((induction) <=>
13.13/2.51	          (((!!) @ (^[Y0 : term > $o]:
13.13/2.51	                      (((!!) @ (^[Y1 : term]:
13.13/2.51	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.51	                                                        (((!!) @ (^[Y3 : term]:
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ Y2))) | 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    ap @ 
13.13/2.51	                                                                    Y2 @ Y3)) | 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ Y3))))))))))))) | 
13.13/2.51	                                    (Y0 @ Y1) | 
13.13/2.51	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.51	                                                        (((Y0 @ (lam @ Y2)) |
13.13/2.51	                                                          (((~) @ (Y0 @ Y2)))))))))) | 
13.13/2.51	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.51	                                                        (((((~) @ (var @ Y2))) |
13.13/2.51	                                                          (Y0 @ Y2)))))))))))))))))) & 
13.13/2.51	        (((((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
13.13/2.51	            (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.51	                          (((!!) @ (^[Y1 : term]:
13.13/2.51	                                      (((((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.51	                                                            (((((~) @ (
13.13/2.51	                                                                ((!!) @ (
13.13/2.51	                                                                 ^[Y3 : subst]:
13.13/2.51	                                                                   ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y4 : term]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y5 : subst]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (sub @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    Y2 @ 
13.13/2.51	                                                                    Y3 @ Y4) @ 
13.13/2.51	                                                                    Y5) =
13.13/2.51	                                                                    (Y2 @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    comp @ 
13.13/2.51	                                                                    Y3 @ Y5) @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    sub @ 
13.13/2.51	                                                                    Y4 @ Y5))))))))))))))) | 
13.13/2.51	                                                              (((~) @ (
13.13/2.51	                                                                ((!!) @ (
13.13/2.51	                                                                 ^[Y3 : term]:
13.13/2.51	                                                                   ((
13.13/2.51	                                                                    (Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    Y2 @ 
13.13/2.51	                                                                    id @ Y3) @ 
13.13/2.51	                                                                    id) |
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    Y3 @ id)))))))))) | 
13.13/2.51	                                                              (Y0 @ id @ 
13.13/2.51	                                                               (lam @ 
13.13/2.51	                                                                (Y2 @ sh @ 
13.13/2.51	                                                                 one)) @ 
13.13/2.51	                                                               id)))))))) | 
13.13/2.51	                                        (Y0 @ id @ 
13.13/2.51	                                         (lam @ 
13.13/2.51	                                          (sub @ Y1 @ (push @ one @ sh))) @ 
13.13/2.51	                                         id) | 
13.13/2.51	                                        (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.51	                                                            (((((~) @ (
13.13/2.51	                                                                Y0 @ id @ 
13.13/2.51	                                                                Y2 @ id))) |
13.13/2.51	                                                              (Y0 @ id @ 
13.13/2.51	                                                              (sub @ Y1 @ 
13.13/2.51	                                                               (push @ Y2 @ 
13.13/2.51	                                                                id)) @ 
13.13/2.51	                                                              id)))))))))))))))) =>
13.13/2.51	              (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.51	                          (((!!) @ (^[Y1 : term]:
13.13/2.51	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.51	                                                            (((((~) @ (
13.13/2.51	                                                                Y0 @ id @ 
13.13/2.51	                                                                Y2 @ id))) |
13.13/2.51	                                                              (Y0 @ id @ 
13.13/2.51	                                                              (sub @ Y1 @ 
13.13/2.51	                                                               (push @ Y2 @ 
13.13/2.51	                                                                id)) @ 
13.13/2.51	                                                              id)))))))) | 
13.13/2.51	                                        (Y0 @ id @ (lam @ Y1) @ id) | 
13.13/2.51	                                        (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.51	                                                            (((Y0 @ id @ 
13.13/2.51	                                                               (lam @ 
13.13/2.51	                                                                (Y2 @ sh @ 
13.13/2.51	                                                                 one)) @ 
13.13/2.51	                                                               id) | 
13.13/2.51	                                                              (((~) @ (
13.13/2.51	                                                                ((!!) @ (
13.13/2.51	                                                                 ^[Y3 : term]:
13.13/2.51	                                                                   ((
13.13/2.51	                                                                    (Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    (
13.13/2.51	                                                                    Y2 @ 
13.13/2.51	                                                                    id @ Y3) @ 
13.13/2.51	                                                                    id) |
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (~) @ (
13.13/2.51	                                                                    Y0 @ 
13.13/2.51	                                                                    id @ 
13.13/2.51	                                                                    Y3 @ id)))))))))) | 
13.13/2.51	                                                              (((~) @ (
13.13/2.51	                                                                ((!!) @ (
13.13/2.51	                                                                 ^[Y3 : subst]:
13.13/2.51	                                                                   ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y4 : term]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (!!) @ (
13.13/2.51	                                                                    ^[Y5 : subst]:
13.13/2.51	                                                                    ((
13.13/2.51	                                                                    (sub @ 
13.13/2.51	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ Y4) @ 
13.13/2.52	                                                                    Y5) =
13.13/2.52	                                                                    (Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))))))) <=>
13.13/2.52	          (hoasinduction_lem3a_lthm))) & 
13.13/2.52	        termmset_gthm & 
13.13/2.52	        (((hoasinduction_lem3aa) <=>
13.13/2.52	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((Y0 @ id @ 
13.13/2.52	                                     (lam @ (sub @ Y1 @ (push @ one @ sh))) @ 
13.13/2.52	                                     id) | 
13.13/2.52	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                        (((((~) @ (Y0 @ id @ 
13.13/2.52	                                                                   Y2 @ id))) |
13.13/2.52	                                                          (Y0 @ id @ 
13.13/2.52	                                                          (sub @ Y1 @ 
13.13/2.52	                                                           (push @ Y2 @ id)) @ 
13.13/2.52	                                                          id)))))))) | 
13.13/2.52	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.52	                                                        (((Y0 @ id @ 
13.13/2.52	                                                           (lam @ 
13.13/2.52	                                                            (Y2 @ sh @ one)) @ 
13.13/2.52	                                                           id) | 
13.13/2.52	                                                          (((~) @ (((!!) @ (
13.13/2.52	                                                                    ^[Y3 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    id @ Y3) @ 
13.13/2.52	                                                                    id) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id)))))))))) | 
13.13/2.52	                                                          (((~) @ (((!!) @ (
13.13/2.52	                                                                    ^[Y3 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ Y4) @ 
13.13/2.52	                                                                    Y5) =
13.13/2.52	                                                                    (Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))))) & 
13.13/2.52	        hoaslamnotap_gthm & hoasinduction_lem3b_gthm & pushprop_lem2v2 & 
13.13/2.52	        hoasinduction_lem3a_gthm & axassoc & pushprop_lthm & 
13.13/2.52	        (((((!!) @ (^[Y0 : term]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((!!) @ (^[Y2 : term]:
13.13/2.52	                                              (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                          (((((Y2) = (Y3))) |
13.13/2.52	                                                            (((ap @ Y0 @ 
13.13/2.52	                                                              Y2) != (ap @ 
13.13/2.52	                                                              Y1 @ Y3))))))))))))))))) <=>
13.13/2.52	          (apinj2))) & 
13.13/2.52	        (((((!!) @ (^[Y0 : term]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((!!) @ (^[Y2 : term]:
13.13/2.52	                                              (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                          (((((ap @ Y0 @ 
13.13/2.52	                                                              Y2) != (ap @ 
13.13/2.52	                                                              Y1 @ Y3))) |
13.13/2.52	                                                            (((Y0) = (Y1))))))))))))))))) <=>
13.13/2.52	          (apinj1))) & 
13.13/2.52	        (((((!!) @ (^[Y0 : term]:
13.13/2.52	                      (((!!) @ (^[Y1 : subst]:
13.13/2.52	                                  (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) <=>
13.13/2.52	          (axvarcons))) & 
13.13/2.52	        hoasinduction_lem2v2_gthm & 
13.13/2.52	        (((pushprop_lem0) <=>
13.13/2.52	          (((!!) @ (^[Y0 : term > $o]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((!!) @ (^[Y2 : subst]:
13.13/2.52	                                              (((~) @ (((!!) @ (^[Y3 : term > $o]:
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y3 @ 
13.13/2.52	                                                                    Y4) <=>
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y1 @ Y2)))))))))))))))))))))))))) & 
13.13/2.52	        (((hoasinduction_lem3v2a_lthm) <=>
13.13/2.52	          (((((!!) @ (^[Y0 : term]:
13.13/2.52	                        (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
13.13/2.52	                                            (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                                (((!!) @ (
13.13/2.52	                                                                  ^[Y3 : subst]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y2 @ Y3)) =
13.13/2.52	                                                                    (Y1 @ 
13.13/2.52	                                                                    Y3 @ Y2))))))))))))))))))) =>
13.13/2.52	            (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
13.13/2.52	              (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                          (((!!) @ (^[Y1 : term > $o]:
13.13/2.52	                                      (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                  (((((~) @ (((!!) @ (
13.13/2.52	                                                              ^[Y3 : 
13.13/2.52	                                                                subst > term > term]:
13.13/2.52	                                                                (((((~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ Y5) @ 
13.13/2.52	                                                                    Y6) =
13.13/2.52	                                                                    (Y3 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y5 @ Y6))))))))))))))) | 
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    id @ Y4) @ 
13.13/2.52	                                                                    id) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y4 @ id)))))))))) | 
13.13/2.52	                                                                  (Y0 @ id @ 
13.13/2.52	                                                                   (lam @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    sh @ one)) @ 
13.13/2.52	                                                                   id)))))))) | 
13.13/2.52	                                                    (((~) @ (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((Y1 @ 
13.13/2.52	                                                                  Y3) <=>
13.13/2.52	                                                                  (Y0 @ id @ 
13.13/2.52	                                                                  Y3 @ id)))))))) | 
13.13/2.52	                                                    (Y1 @ (lam @ Y2)) | 
13.13/2.52	                                                    (((~) @ (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((Y1 @ 
13.13/2.52	                                                                  (sub @ 
13.13/2.52	                                                                   Y2 @ 
13.13/2.52	                                                                   (push @ 
13.13/2.52	                                                                    Y3 @ id))) |
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    Y1 @ Y3))))))))))))))))))))))))))) & 
13.13/2.52	        hoasinduction_lem1_lthm & 
13.13/2.52	        (((((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
13.13/2.52	            (((((!!) @ (^[Y0 : term > $o]:
13.13/2.52	                          (((!!) @ (^[Y1 : term]:
13.13/2.52	                                      (((!!) @ (^[Y2 : subst]:
13.13/2.52	                                                  (((((~) @ (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((!!) @ (
13.13/2.52	                                                                  ^[Y4 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y3))) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    ap @ 
13.13/2.52	                                                                    Y3 @ Y4)) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y4))))))))))))) | 
13.13/2.52	                                                    (((~) @ (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((((~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y4 @ id))) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y4)))))))))) |
13.13/2.52	                                                                  (Y0 @ 
13.13/2.52	                                                                  (lam @ Y3))))))))) | 
13.13/2.52	                                                    (((~) @ (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((Y0 @ 
13.13/2.52	                                                                  (sub @ 
13.13/2.52	                                                                   Y3 @ Y2)) |
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    var @ Y3)))))))))) | 
13.13/2.52	                                                    (Y0 @ (sub @ Y1 @ Y2))))))))))))) =>
13.13/2.52	              (((!!) @ (^[Y0 : term > $o]:
13.13/2.52	                          (((!!) @ (^[Y1 : term]:
13.13/2.52	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                            (((((~) @ (
13.13/2.52	                                                                var @ Y2))) |
13.13/2.52	                                                              (Y0 @ Y2)))))))) | 
13.13/2.52	                                        (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                            (((((~) @ (
13.13/2.52	                                                                ((!!) @ (
13.13/2.52	                                                                 ^[Y3 : term]:
13.13/2.52	                                                                   ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y3 @ id))) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y3)))))))))) |
13.13/2.52	                                                              (Y0 @ 
13.13/2.52	                                                              (lam @ Y2))))))))) | 
13.13/2.52	                                        (Y0 @ Y1) | 
13.13/2.52	                                        (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                            (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((((~) @ (
13.13/2.52	                                                                    Y0 @ Y2))) | 
13.13/2.52	                                                                  (Y0 @ 
13.13/2.52	                                                                   (ap @ 
13.13/2.52	                                                                    Y2 @ Y3)) | 
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    Y0 @ Y3))))))))))))))))))))))))) <=>
13.13/2.52	          (induction2_lthm))) & 
13.13/2.52	        pushprop & 
13.13/2.52	        (((hoasinduction_lem3a) <=>
13.13/2.52	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                        (((((~) @ (Y0 @ id @ 
13.13/2.52	                                                                   Y2 @ id))) |
13.13/2.52	                                                          (Y0 @ id @ 
13.13/2.52	                                                          (sub @ Y1 @ 
13.13/2.52	                                                           (push @ Y2 @ id)) @ 
13.13/2.52	                                                          id)))))))) | 
13.13/2.52	                                    (Y0 @ id @ (lam @ Y1) @ id) | 
13.13/2.52	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.52	                                                        (((Y0 @ id @ 
13.13/2.52	                                                           (lam @ 
13.13/2.52	                                                            (Y2 @ sh @ one)) @ 
13.13/2.52	                                                           id) | 
13.13/2.52	                                                          (((~) @ (((!!) @ (
13.13/2.52	                                                                    ^[Y3 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    id @ Y3) @ 
13.13/2.52	                                                                    id)))))))) | 
13.13/2.52	                                                          (((~) @ (((!!) @ (
13.13/2.52	                                                                    ^[Y3 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ Y4) @ 
13.13/2.52	                                                                    Y5) =
13.13/2.52	                                                                    (Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y5)))))))))))))))))))))))))))))))) & 
13.13/2.52	        hoasinduction_lem1_gthm & 
13.13/2.52	        (((((!!) @ (^[Y0 : subst > term > term]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((!!) @ (^[Y2 : term]:
13.13/2.52	                                              (((((lam @ (Y0 @ sh @ one)) !=
13.13/2.52	                                                  (ap @ (sub @ Y1 @ id) @ Y2))) |
13.13/2.52	                                                (((~) @ (((!!) @ (^[Y3 : subst]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    Y3 @ Y4) @ 
13.13/2.52	                                                                    Y5) =
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y5)))))))))))))))))))))))))) <=>
13.13/2.52	          (hoaslamnotap))) & 
13.13/2.52	        (((induction2) <=>
13.13/2.52	          (((!!) @ (^[Y0 : term > $o]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                        (((((~) @ (var @ Y2))) |
13.13/2.52	                                                          (Y0 @ Y2)))))))) | 
13.13/2.52	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                        (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    ap @ 
13.13/2.52	                                                                    Y2 @ Y3)) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y3))) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y2))))))))))))) | 
13.13/2.52	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                        (((((~) @ (((!!) @ (
13.13/2.52	                                                                    ^[Y3 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y3))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y3 @ id)))))))))) |
13.13/2.52	                                                          (Y0 @ (lam @ Y2))))))))) | 
13.13/2.52	                                    (Y0 @ Y1))))))))))) & 
13.13/2.52	        pushprop_lem3v2 & pushprop_lem2v2_gthm & 
13.13/2.52	        (((pushprop_lem1_lthm) <=>
13.13/2.52	          (((((!!) @ (^[Y0 : term]:
13.13/2.52	                        (((!!) @ (^[Y1 : subst]:
13.13/2.52	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
13.13/2.52	            (((((!!) @ (^[Y0 : term]:
13.13/2.52	                          (((!!) @ (^[Y1 : subst]:
13.13/2.52	                                      (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) =>
13.13/2.52	              (((!!) @ (^[Y0 : term > $o]:
13.13/2.52	                          (((!!) @ (^[Y1 : term > $o]:
13.13/2.52	                                      (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                  (((!!) @ (^[Y3 : subst]:
13.13/2.52	                                                              (((!!) @ (
13.13/2.52	                                                                ^[Y4 : term]:
13.13/2.52	                                                                  (((Y1 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y4 @ Y3))) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y2)))))))))))))))))))))))))) & 
13.13/2.52	        (((((!!) @ (^[Y0 : term]:
13.13/2.52	                      (((!!) @ (^[Y1 : subst]:
13.13/2.52	                                  (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) <=>
13.13/2.52	          (axshiftcons))) & 
13.13/2.52	        (((termmset) <=>
13.13/2.52	          (((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))))) & 
13.13/2.52	        hoasapnotvar_lthm & 
13.13/2.52	        (((hoasinduction_lem3v2_lthm) <=>
13.13/2.52	          (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
13.13/2.52	            (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                        (((!!) @ (^[Y1 : term > $o]:
13.13/2.52	                                    (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                (((((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y1 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y3 @ id))) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y1 @ Y3)))))))))) | 
13.13/2.52	                                                  (Y1 @ (lam @ Y2)) | 
13.13/2.52	                                                  (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y1 @ 
13.13/2.52	                                                                    Y3) <=>
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id)))))))) | 
13.13/2.52	                                                  (((~) @ (((!!) @ (^[Y3 : 
13.13/2.52	                                                                    subst > 
13.13/2.52	                                                                    term > term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    id @ Y4) @ 
13.13/2.52	                                                                    id) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y4 @ id)))))))))) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    lam @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    sh @ one)) @ 
13.13/2.52	                                                                    id) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ Y5) @ 
13.13/2.52	                                                                    Y6) =
13.13/2.52	                                                                    (Y3 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y5 @ Y6)))))))))))))))))))))) | 
13.13/2.52	                                                  (((~) @ (((!!) @ (^[Y3 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    Y5))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y6 @ Y5)))))))))))))))))) | 
13.13/2.52	                                                  (((~) @ (((!!) @ (^[Y3 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y6 @ Y5)))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    Y5)))))))))))))))))))))))))))))))) & 
13.13/2.52	        (((((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                        (((~) @ (((!!) @ (^[Y1 : term > $o]:
13.13/2.52	                                            (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                                (((Y1 @ 
13.13/2.52	                                                                  Y2) <=>
13.13/2.52	                                                                  (Y0 @ id @ 
13.13/2.52	                                                                  Y2 @ id)))))))))))))))) =>
13.13/2.52	            (((((!!) @ (^[Y0 : term > $o]:
13.13/2.52	                          (((!!) @ (^[Y1 : term]:
13.13/2.52	                                      (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                            (((((~) @ (
13.13/2.52	                                                                var @ Y2))) |
13.13/2.52	                                                              (Y0 @ Y2)))))))) | 
13.13/2.52	                                        (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                            (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((((~) @ (
13.13/2.52	                                                                    Y0 @ Y2))) | 
13.13/2.52	                                                                  (Y0 @ 
13.13/2.52	                                                                   (ap @ 
13.13/2.52	                                                                    Y2 @ Y3)) | 
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    Y0 @ Y3))))))))))))) | 
13.13/2.52	                                        (Y0 @ Y1) | 
13.13/2.52	                                        (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                            (((((~) @ (
13.13/2.52	                                                                ((!!) @ (
13.13/2.52	                                                                 ^[Y3 : term]:
13.13/2.52	                                                                   ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ Y3))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y3 @ id)))))))))) |
13.13/2.52	                                                              (Y0 @ 
13.13/2.52	                                                              (lam @ Y2))))))))))))))))) =>
13.13/2.52	              (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
13.13/2.52	                (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                              (((!!) @ (^[Y1 : term > $o]:
13.13/2.52	                                          (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                      (((((~) @ (((!!) @ (
13.13/2.52	                                                                  ^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y1 @ Y3))) |
13.13/2.52	                                                                    (Y1 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y3 @ id)))))))))) | 
13.13/2.52	                                                        (Y1 @ (lam @ Y2)) | 
13.13/2.52	                                                        (((~) @ (((!!) @ (
13.13/2.52	                                                                  ^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (Y1 @ 
13.13/2.52	                                                                    Y3) <=>
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id)))))))) | 
13.13/2.52	                                                        (((~) @ (((!!) @ (
13.13/2.52	                                                                  ^[Y3 : 
13.13/2.52	                                                                    subst > 
13.13/2.52	                                                                    term > term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y4 @ id))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    id @ Y4) @ 
13.13/2.52	                                                                    id)))))))) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    lam @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    sh @ one)) @ 
13.13/2.52	                                                                    id) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ Y5) @ 
13.13/2.52	                                                                    Y6) =
13.13/2.52	                                                                    (Y3 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y5 @ Y6))))))))))))))))))))))))))))))))) =>
13.13/2.52	                  (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                              (((!!) @ (^[Y1 : term]:
13.13/2.52	                                          (((((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.52	                                                                (((!!) @ (
13.13/2.52	                                                                  ^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y2 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    Y4))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y5 @ Y4)))))))))))))))))) | 
13.13/2.52	                                            (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                                (((((~) @ (
13.13/2.52	                                                                    var @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ id)))) |
13.13/2.52	                                                                  (Y0 @ id @ 
13.13/2.52	                                                                  Y2 @ id)))))))) | 
13.13/2.52	                                            (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                                (((!!) @ (
13.13/2.52	                                                                  ^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id))) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    ap @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ id) @ 
13.13/2.52	                                                                    Y3) @ id) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y2 @ id))))))))))))) | 
13.13/2.52	                                            (Y0 @ id @ Y1 @ id) | 
13.13/2.52	                                            (((~) @ (((!!) @ (^[Y2 : 
13.13/2.52	                                                                subst > term > term]:
13.13/2.52	                                                                (((((~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y3 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ Y4) @ 
13.13/2.52	                                                                    Y5) =
13.13/2.52	                                                                    (Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y5))))))))))))))) | 
13.13/2.52	                                                                  (Y0 @ id @ 
13.13/2.52	                                                                   (lam @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    sh @ one)) @ 
13.13/2.52	                                                                   id) | 
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y3 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    id @ Y3) @ 
13.13/2.52	                                                                    id))))))))))))))) | 
13.13/2.52	                                            (((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.52	                                                                (((!!) @ (
13.13/2.52	                                                                  ^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y5 @ Y4)))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y2 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    Y4))))))))))))))))))))))))))))))))) <=>
13.13/2.52	          (hoasinduction_lthm_3))) & 
13.13/2.52	        (((axvarid) <=> (((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))))) & 
13.13/2.52	        (((pushprop_lem0_lthm) <=>
13.13/2.52	          (((!!) @ (^[Y0 : term > $o]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((!!) @ (^[Y2 : subst]:
13.13/2.52	                                              (((~) @ (((!!) @ (^[Y3 : term > $o]:
13.13/2.52	                                                                  (((~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y3 @ 
13.13/2.52	                                                                    Y4) <=>
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y1 @ Y2)))))))))))))))))))))))))) & 
13.13/2.52	        (((hoasinduction_lem3v2) <=>
13.13/2.52	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                      (((!!) @ (^[Y1 : term > $o]:
13.13/2.52	                                  (((!!) @ (^[Y2 : term]:
13.13/2.52	                                              (((((~) @ (((!!) @ (^[Y3 : subst]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y6 @ Y5)))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    Y5))))))))))))))))) | 
13.13/2.52	                                                (((~) @ (((!!) @ (^[Y3 : subst]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y6 @ Y5)) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    Y5))))))))))))))))))) | 
13.13/2.52	                                                (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (Y1 @ 
13.13/2.52	                                                                    Y3) <=>
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id)))))))) | 
13.13/2.52	                                                (Y1 @ (lam @ Y2)) | 
13.13/2.52	                                                (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y1 @ Y3))) |
13.13/2.52	                                                                    (Y1 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    push @ 
13.13/2.52	                                                                    Y3 @ id)))))))))) | 
13.13/2.52	                                                (((~) @ (((!!) @ (^[Y3 : 
13.13/2.52	                                                                    subst > 
13.13/2.52	                                                                    term > term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y6 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    Y4 @ Y5) @ 
13.13/2.52	                                                                    Y6) =
13.13/2.52	                                                                    (Y3 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y4 @ Y6) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y5 @ Y6))))))))))))))) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    lam @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    sh @ one)) @ 
13.13/2.52	                                                                    id) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y3 @ 
13.13/2.52	                                                                    id @ Y4) @ 
13.13/2.52	                                                                    id) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y4 @ id)))))))))))))))))))))))))))))) & 
13.13/2.52	        ulamvarsh & substmonoid_gthm & 
13.13/2.52	        (((~) @ (hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ 
13.13/2.52	                 (d2subst @ d_id)))) & 
13.13/2.52	        pushprop_lem2v2_lthm & induction2_gthm & 
13.13/2.52	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                      (((!!) @ (^[Y1 : term]:
13.13/2.52	                                  (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                        (((!!) @ (^[Y3 : term]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    ap @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y2 @ id) @ 
13.13/2.52	                                                                    Y3) @ id) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id))) | 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y2 @ id))))))))))))) | 
13.13/2.52	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.52	                                                        (((Y0 @ id @ 
13.13/2.52	                                                           (lam @ 
13.13/2.52	                                                            (Y2 @ sh @ one)) @ 
13.13/2.52	                                                           id) | 
13.13/2.52	                                                          (((~) @ (((!!) @ (
13.13/2.52	                                                                    ^[Y3 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id))) |
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    id @ Y3) @ 
13.13/2.52	                                                                    id)))))))) | 
13.13/2.52	                                                          (((~) @ (((!!) @ (
13.13/2.52	                                                                    ^[Y3 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ Y4) @ 
13.13/2.52	                                                                    Y5) =
13.13/2.52	                                                                    (Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
13.13/2.52	                                    (Y0 @ id @ Y1 @ id))))))))) <=>
13.13/2.52	          (hoasinduction_no_psi_cond))) & 
13.13/2.52	        lamnotvar & 
13.13/2.52	        (((((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))) &
13.13/2.52	            (((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))))) <=>
13.13/2.52	          (substmonoid))) & 
13.13/2.52	        (((((!!) @ (^[Y0 : term]:
13.13/2.52	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
13.13/2.52	                                          (((Y1 @ sh @ one) != (sub @ Y0 @ 
13.13/2.52	                                            (push @ one @ sh)))))))))))) <=>
13.13/2.52	          (hoasinduction_lem3b))) & 
13.13/2.52	        hoasinduction_lem2_gthm & hoasinduction_lem3_gthm & 
13.13/2.52	        (((((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))) =>
13.13/2.52	            (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) =>
13.13/2.52	              (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) &
13.13/2.52	                (((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))))))))) <=>
13.13/2.52	          (substmonoid_lthm))) & 
13.13/2.52	        (((hoasinduction_lem0_lthm) <=>
13.13/2.52	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                      (((~) @ (((!!) @ (^[Y1 : term > $o]:
13.13/2.52	                                          (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                              (((Y1 @ Y2) <=>
13.13/2.52	                                                                (Y0 @ id @ 
13.13/2.52	                                                                Y2 @ id)))))))))))))))))) & 
13.13/2.52	        hoaslaminj_gthm & 
13.13/2.52	        (((axidl) <=> (((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ id @ Y0)))))))) & 
13.13/2.52	        hoaslamnotvar & hoasapinj1_gthm & (((~) @ lamnotap)) & 
13.13/2.52	        hoasapinj2_gthm & hoasinduction_lem2_lthm & axabs & pushprop_gthm & 
13.13/2.52	        (((hoasinduction_lem3_lthm) <=>
13.13/2.52	          (((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
13.13/2.52	            (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                          (((!!) @ (^[Y1 : term]:
13.13/2.52	                                      (((((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.52	                                                            (((Y0 @ id @ 
13.13/2.52	                                                               (lam @ 
13.13/2.52	                                                                (Y2 @ sh @ 
13.13/2.52	                                                                 one)) @ 
13.13/2.52	                                                               id) | 
13.13/2.52	                                                              (((~) @ (
13.13/2.52	                                                                ((!!) @ (
13.13/2.52	                                                                 ^[Y3 : term]:
13.13/2.52	                                                                   ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    id @ Y3) @ 
13.13/2.52	                                                                    id) |
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (~) @ (
13.13/2.52	                                                                    Y0 @ 
13.13/2.52	                                                                    id @ 
13.13/2.52	                                                                    Y3 @ id)))))))))) | 
13.13/2.52	                                                              (((~) @ (
13.13/2.52	                                                                ((!!) @ (
13.13/2.52	                                                                 ^[Y3 : subst]:
13.13/2.52	                                                                   ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y4 : term]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (sub @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    Y2 @ 
13.13/2.52	                                                                    Y3 @ Y4) @ 
13.13/2.52	                                                                    Y5) =
13.13/2.52	                                                                    (Y2 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y3 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.52	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
13.13/2.52	                                        (Y0 @ id @ 
13.13/2.52	                                         (lam @ 
13.13/2.52	                                          (sub @ Y1 @ (push @ one @ sh))) @ 
13.13/2.52	                                         id) | 
13.13/2.52	                                        (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.52	                                                            (((Y0 @ id @ 
13.13/2.52	                                                              (sub @ Y1 @ 
13.13/2.52	                                                               (push @ Y2 @ 
13.13/2.52	                                                                id)) @ 
13.13/2.52	                                                              id) |
13.13/2.52	                                                              (((~) @ (
13.13/2.52	                                                                Y0 @ id @ 
13.13/2.52	                                                                Y2 @ id)))))))))))))))))) =>
13.13/2.52	              (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.52	                          (((!!) @ (^[Y1 : term]:
13.13/2.52	                                      (((((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.52	                                                            (((!!) @ (
13.13/2.52	                                                              ^[Y3 : term]:
13.13/2.52	                                                                (((!!) @ (
13.13/2.52	                                                                  ^[Y4 : subst]:
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (
13.13/2.52	                                                                    (!!) @ (
13.13/2.52	                                                                    ^[Y5 : subst]:
13.13/2.52	                                                                    ((
13.13/2.52	                                                                    (Y0 @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    comp @ 
13.13/2.52	                                                                    Y2 @ Y5) @ 
13.13/2.52	                                                                    (
13.13/2.52	                                                                    sub @ 
13.13/2.53	                                                                    Y3 @ Y5) @ 
13.13/2.53	                                                                    Y4) |
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y5 @ Y4)))))))))))))))))))) | 
13.13/2.53	                                        (((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.53	                                                            (((!!) @ (
13.13/2.53	                                                              ^[Y3 : term]:
13.13/2.53	                                                                (((!!) @ (
13.13/2.53	                                                                  ^[Y4 : subst]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y2 @ Y5) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y3 @ Y5) @ 
13.13/2.53	                                                                    Y4))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y5 @ Y4)))))))))))))))))) | 
13.13/2.53	                                        (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.53	                                                            (((((~) @ (
13.13/2.53	                                                                ((!!) @ (
13.13/2.53	                                                                 ^[Y3 : subst]:
13.13/2.53	                                                                   ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (sub @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    Y3 @ Y4) @ 
13.13/2.53	                                                                    Y5) =
13.13/2.53	                                                                    (Y2 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y3 @ Y5) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y4 @ Y5))))))))))))))) | 
13.13/2.53	                                                              (Y0 @ id @ 
13.13/2.53	                                                               (lam @ 
13.13/2.53	                                                                (Y2 @ sh @ 
13.13/2.53	                                                                 one)) @ 
13.13/2.53	                                                               id) | 
13.13/2.53	                                                              (((~) @ (
13.13/2.53	                                                                ((!!) @ (
13.13/2.53	                                                                 ^[Y3 : term]:
13.13/2.53	                                                                   ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y3 @ id))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    id @ Y3) @ 
13.13/2.53	                                                                    id))))))))))))))) | 
13.13/2.53	                                        (Y0 @ id @ (lam @ Y1) @ id) | 
13.13/2.53	                                        (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                            (((((~) @ (
13.13/2.53	                                                                Y0 @ id @ 
13.13/2.53	                                                                Y2 @ id))) |
13.13/2.53	                                                              (Y0 @ id @ 
13.13/2.53	                                                              (sub @ Y1 @ 
13.13/2.53	                                                               (push @ Y2 @ 
13.13/2.53	                                                                id)) @ 
13.13/2.53	                                                              id)))))))))))))))))))))) & 
13.13/2.53	        (((laminj) <=>
13.13/2.53	          (((!!) @ (^[Y0 : term]:
13.13/2.53	                      (((!!) @ (^[Y1 : term]:
13.13/2.53	                                  (((((lam @ Y0) != (lam @ Y1))) |
13.13/2.53	                                    (((Y0) = (Y1))))))))))))) & 
13.13/2.53	        (((pushprop_lem1) <=>
13.13/2.53	          (((!!) @ (^[Y0 : term > $o]:
13.13/2.53	                      (((!!) @ (^[Y1 : term > $o]:
13.13/2.53	                                  (((!!) @ (^[Y2 : term]:
13.13/2.53	                                              (((!!) @ (^[Y3 : subst]:
13.13/2.53	                                                          (((!!) @ (^[Y4 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ Y2))) |
13.13/2.53	                                                                    (Y1 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    push @ 
13.13/2.53	                                                                    Y4 @ Y3)))))))))))))))))))))) & 
13.13/2.53	        (((((!!) @ (^[Y0 : subst]: (((Y0) = (comp @ Y0 @ id)))))) <=> (axidr))) & 
13.13/2.53	        (((((!!) @ (^[Y0 : subst]:
13.13/2.53	                      (((Y0) = (push @ (sub @ one @ Y0) @ (comp @ sh @ Y0))))))) <=>
13.13/2.53	          (axscons))) & 
13.13/2.53	        (((hoaslaminj_lthm) <=>
13.13/2.53	          (((((!!) @ (^[Y0 : term]:
13.13/2.53	                        (((!!) @ (^[Y1 : subst]:
13.13/2.53	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
13.13/2.53	            (((((!!) @ (^[Y0 : term]:
13.13/2.53	                          (((!!) @ (^[Y1 : subst]:
13.13/2.53	                                      (((Y1) = (comp @ sh @ (push @ Y0 @ Y1)))))))))) =>
13.13/2.53	              (((((!!) @ (^[Y0 : term]:
13.13/2.53	                            (((!!) @ (^[Y1 : term]:
13.13/2.53	                                        (((((Y0) = (Y1))) |
13.13/2.53	                                          (((lam @ Y0) != (lam @ Y1))))))))))) =>
13.13/2.53	                (((!!) @ (^[Y0 : subst > term > term]:
13.13/2.53	                            (((!!) @ (^[Y1 : subst > term > term]:
13.13/2.53	                                        (((!!) @ (^[Y2 : subst]:
13.13/2.53	                                                    (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                                (((((~) @ (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (sub @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y1 @ 
13.13/2.53	                                                                    Y4 @ Y5) @ 
13.13/2.53	                                                                    Y6) =
13.13/2.53	                                                                    (Y1 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y5 @ Y6))))))))))))))) | 
13.13/2.53	                                                                  (((Y0 @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    Y3) =
13.13/2.53	                                                                    (Y1 @ 
13.13/2.53	                                                                    Y2 @ Y3))) | 
13.13/2.53	                                                                  (((lam @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    sh @ one)) !=
13.13/2.53	                                                                    (lam @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y1 @ 
13.13/2.53	                                                                    sh @ one)))) | 
13.13/2.53	                                                                  (((~) @ (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (sub @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    Y4 @ Y5) @ 
13.13/2.53	                                                                    Y6) =
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y5 @ Y6))))))))))))))))))))))))))))))))))))) & 
13.13/2.53	        (((((((!!) @ (^[Y0 : term]: (((Y0) = (sub @ Y0 @ id)))))) =>
13.13/2.53	            (((((!!) @ (^[Y0 : term]:
13.13/2.53	                          (((!!) @ (^[Y1 : term]:
13.13/2.53	                                      (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                  (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                              (((((ap @ Y0 @ 
13.13/2.53	                                                                  Y2) !=
13.13/2.53	                                                                  (ap @ Y1 @ 
13.13/2.53	                                                                  Y3))) |
13.13/2.53	                                                                (((Y0) = (Y1))))))))))))))))) =>
13.13/2.53	              (((!!) @ (^[Y0 : term]:
13.13/2.53	                          (((!!) @ (^[Y1 : term]:
13.13/2.53	                                      (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                  (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                              (((((Y0) = (Y1))) |
13.13/2.53	                                                                (((ap @ 
13.13/2.53	                                                                  (sub @ 
13.13/2.53	                                                                   Y0 @ id) @ 
13.13/2.53	                                                                  Y2) !=
13.13/2.53	                                                                  (ap @ 
13.13/2.53	                                                                  (sub @ 
13.13/2.53	                                                                   Y1 @ id) @ 
13.13/2.53	                                                                  Y3))))))))))))))))))))) <=>
13.13/2.53	          (hoasapinj1_lthm))) & 
13.13/2.53	        (((hoasinduction_lem3v2a) <=>
13.13/2.53	          (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.53	                      (((!!) @ (^[Y1 : term > $o]:
13.13/2.53	                                  (((!!) @ (^[Y2 : term]:
13.13/2.53	                                              (((((~) @ (((!!) @ (^[Y3 : 
13.13/2.53	                                                                    subst > 
13.13/2.53	                                                                    term > term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    id @ Y4) @ 
13.13/2.53	                                                                    id) |
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y4 @ id)))))))))) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    lam @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    sh @ one)) @ 
13.13/2.53	                                                                    id) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (sub @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    Y4 @ Y5) @ 
13.13/2.53	                                                                    Y6) =
13.13/2.53	                                                                    (Y3 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y5 @ Y6)))))))))))))))))))))) | 
13.13/2.53	                                                (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (Y1 @ 
13.13/2.53	                                                                    Y3) <=>
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y3 @ id)))))))) | 
13.13/2.53	                                                (Y1 @ (lam @ Y2)) | 
13.13/2.53	                                                (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y1 @ Y3))) |
13.13/2.53	                                                                    (Y1 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    push @ 
13.13/2.53	                                                                    Y3 @ id))))))))))))))))))))))) & 
13.13/2.53	        (((((((!!) @ (^[Y0 : term]:
13.13/2.53	                        (((!!) @ (^[Y1 : term]:
13.13/2.53	                                    (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                            (((((ap @ Y0 @ 
13.13/2.53	                                                                Y2) != (ap @ 
13.13/2.53	                                                                Y1 @ Y3))) |
13.13/2.53	                                                              (((Y2) = (Y3))))))))))))))))) =>
13.13/2.53	            (((!!) @ (^[Y0 : term]:
13.13/2.53	                        (((!!) @ (^[Y1 : term]:
13.13/2.53	                                    (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                            (((((Y2) = (Y3))) |
13.13/2.53	                                                              (((ap @ 
13.13/2.53	                                                                (sub @ Y0 @ 
13.13/2.53	                                                                 id) @ 
13.13/2.53	                                                                Y2) != (ap @ 
13.13/2.53	                                                                (sub @ Y1 @ 
13.13/2.53	                                                                 id) @ 
13.13/2.53	                                                                Y3))))))))))))))))))) <=>
13.13/2.53	          (hoasapinj2_lthm))) & 
13.13/2.53	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.53	                      (((!!) @ (^[Y1 : term > $o]:
13.13/2.53	                                  (((!!) @ (^[Y2 : term]:
13.13/2.53	                                              (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                          (((((~) @ (
13.13/2.53	                                                              ((!!) @ (
13.13/2.53	                                                               ^[Y4 : subst]:
13.13/2.53	                                                                 (((!!) @ (
13.13/2.53	                                                                   ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y7 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y4 @ Y7) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y5 @ Y7) @ 
13.13/2.53	                                                                    Y6))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    Y4 @ 
13.13/2.53	                                                                    Y5 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y7 @ Y6)))))))))))))))))) | 
13.13/2.53	                                                            (((~) @ (Y1 @ Y2))) | 
13.13/2.53	                                                            (Y1 @ 
13.13/2.53	                                                             (ap @ Y2 @ Y3)) | 
13.13/2.53	                                                            (((~) @ (Y1 @ Y3))) | 
13.13/2.53	                                                            (((~) @ (
13.13/2.53	                                                              ((!!) @ (
13.13/2.53	                                                               ^[Y4 : term]:
13.13/2.53	                                                                 (((Y1 @ 
13.13/2.53	                                                                   Y4) <=>
13.13/2.53	                                                                   (Y0 @ 
13.13/2.53	                                                                   id @ Y4 @ 
13.13/2.53	                                                                   id)))))))) | 
13.13/2.53	                                                            (((~) @ (
13.13/2.53	                                                              ((!!) @ (
13.13/2.53	                                                               ^[Y4 : term]:
13.13/2.53	                                                                 (((!!) @ (
13.13/2.53	                                                                   ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    ap @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y4 @ id) @ 
13.13/2.53	                                                                    Y5) @ id) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y5 @ id))) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y4 @ id))))))))))))) | 
13.13/2.53	                                                            (((~) @ (
13.13/2.53	                                                              ((!!) @ (
13.13/2.53	                                                               ^[Y4 : subst]:
13.13/2.53	                                                                 (((!!) @ (
13.13/2.53	                                                                   ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y7 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y4 @ Y7) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y5 @ Y7) @ 
13.13/2.53	                                                                    Y6) |
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    Y4 @ 
13.13/2.53	                                                                    Y5 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y7 @ Y6)))))))))))))))))))))))))))))))))) <=>
13.13/2.53	          (hoasinduction_lem2v2))) & 
13.13/2.53	        axclos & hoaslamnotvar_gthm & pushprop_lem1v2_gthm & 
13.13/2.53	        (((hoasinduction_lem3b_lthm) <=>
13.13/2.53	          (((!!) @ (^[Y0 : term]:
13.13/2.53	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
13.13/2.53	                                          (((Y1 @ sh @ one) != (sub @ Y0 @ 
13.13/2.53	                                            (push @ one @ sh)))))))))))))) & 
13.13/2.53	        pushprop_lem3v2_lthm & hoasapnotvar & 
13.13/2.53	        (((((((!!) @ (^[Y0 : term]:
13.13/2.53	                        (((!!) @ (^[Y1 : subst]:
13.13/2.53	                                    (((Y0) = (sub @ one @ (push @ Y0 @ Y1)))))))))) =>
13.13/2.53	            (((!!) @ (^[Y0 : term > $o]:
13.13/2.53	                        (((!!) @ (^[Y1 : term > $o]:
13.13/2.53	                                    (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                (((!!) @ (^[Y3 : subst]:
13.13/2.53	                                                            (((((~) @ (
13.13/2.53	                                                                Y0 @ Y2))) | 
13.13/2.53	                                                              (((~) @ (
13.13/2.53	                                                                ((!!) @ (
13.13/2.53	                                                                 ^[Y4 : term]:
13.13/2.53	                                                                   ((
13.13/2.53	                                                                    (Y1 @ 
13.13/2.53	                                                                    Y4) <=>
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y4 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    push @ 
13.13/2.53	                                                                    Y2 @ Y3)))))))))) | 
13.13/2.53	                                                              (Y1 @ one))))))))))))))))) <=>
13.13/2.53	          (pushprop_lem1v2_lthm))) & 
13.13/2.53	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.53	                      (((!!) @ (^[Y1 : term]:
13.13/2.53	                                  (((!!) @ (^[Y2 : term]:
13.13/2.53	                                              (((((~) @ (((!!) @ (^[Y3 : subst]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    Y4 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y6 @ Y5)))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y3 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    Y5))))))))))))))))) | 
13.13/2.53	                                                (((~) @ (((!!) @ (^[Y3 : subst]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y3 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    Y5))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    Y4 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y6 @ Y5)))))))))))))))))) | 
13.13/2.53	                                                (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y3 @ id))) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    ap @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y3 @ id) @ 
13.13/2.53	                                                                    Y4) @ id) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y4 @ id))))))))))))) | 
13.13/2.53	                                                (((~) @ (Y0 @ id @ Y1 @ id))) | 
13.13/2.53	                                                (Y0 @ id @ (ap @ Y1 @ Y2) @ 
13.13/2.53	                                                 id) | 
13.13/2.53	                                                (((~) @ (Y0 @ id @ Y2 @ id)))))))))))))) <=>
13.13/2.53	          (hoasinduction_lem2))) & 
13.13/2.53	        (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.53	                      (((!!) @ (^[Y1 : term]:
13.13/2.53	                                  (((((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.53	                                                        (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y5 @ Y4)))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y2 @ Y5) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y3 @ Y5) @ 
13.13/2.53	                                                                    Y4))))))))))))))))) | 
13.13/2.53	                                    (((~) @ (((!!) @ (^[Y2 : subst > term > term]:
13.13/2.53	                                                        (((((~) @ (((!!) @ (
13.13/2.53	                                                                    ^[Y3 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y3 @ id))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    id @ Y3) @ 
13.13/2.53	                                                                    id)))))))) | 
13.13/2.53	                                                          (Y0 @ id @ 
13.13/2.53	                                                           (lam @ 
13.13/2.53	                                                            (Y2 @ sh @ one)) @ 
13.13/2.53	                                                           id) | 
13.13/2.53	                                                          (((~) @ (((!!) @ (
13.13/2.53	                                                                    ^[Y3 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (sub @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    Y3 @ Y4) @ 
13.13/2.53	                                                                    Y5) =
13.13/2.53	                                                                    (Y2 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y3 @ Y5) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
13.13/2.53	                                    (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                        (((Y0 @ id @ 
13.13/2.53	                                                          (sub @ Y1 @ 
13.13/2.53	                                                           (push @ Y2 @ id)) @ 
13.13/2.53	                                                          id) |
13.13/2.53	                                                          (((~) @ (Y0 @ id @ 
13.13/2.53	                                                                   Y2 @ id)))))))))) | 
13.13/2.53	                                    (Y0 @ id @ (lam @ Y1) @ id) | 
13.13/2.53	                                    (((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.53	                                                        (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y4 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y2 @ Y5) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y3 @ Y5) @ 
13.13/2.53	                                                                    Y4))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y5 @ Y4)))))))))))))))))))))))))) <=>
13.13/2.53	          (hoasinduction_lem3))) & 
13.13/2.53	        induction2lem_gthm & 
13.13/2.53	        (((((!!) @ (^[Y0 : subst > term > term]:
13.13/2.53	                      (((!!) @ (^[Y1 : subst > term > term]:
13.13/2.53	                                  (((!!) @ (^[Y2 : subst]:
13.13/2.53	                                              (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                          (((((~) @ (
13.13/2.53	                                                              ((!!) @ (
13.13/2.53	                                                               ^[Y4 : subst]:
13.13/2.53	                                                                 (((!!) @ (
13.13/2.53	                                                                   ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (sub @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    Y4 @ Y5) @ 
13.13/2.53	                                                                    Y6) =
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y5 @ Y6))))))))))))))) | 
13.13/2.53	                                                            (((~) @ (
13.13/2.53	                                                              ((!!) @ (
13.13/2.53	                                                               ^[Y4 : subst]:
13.13/2.53	                                                                 (((!!) @ (
13.13/2.53	                                                                   ^[Y5 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (sub @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y1 @ 
13.13/2.53	                                                                    Y4 @ Y5) @ 
13.13/2.53	                                                                    Y6) =
13.13/2.53	                                                                    (Y1 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y5 @ Y6))))))))))))))) | 
13.13/2.53	                                                            (((Y0 @ Y2 @ 
13.13/2.53	                                                              Y3) = (Y1 @ 
13.13/2.53	                                                              Y2 @ Y3))) | 
13.13/2.53	                                                            (((lam @ 
13.13/2.53	                                                              (Y0 @ sh @ one)) !=
13.13/2.53	                                                              (lam @ 
13.13/2.53	                                                              (Y1 @ sh @ one)))))))))))))))))) <=>
13.13/2.53	          (hoaslaminj))) & 
13.13/2.53	        (((((((!!) @ (^[Y0 : term > $o]:
13.13/2.53	                        (((!!) @ (^[Y1 : term]:
13.13/2.53	                                    (((((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                          (((Y0 @ 
13.13/2.53	                                                            (lam @ Y2)) |
13.13/2.53	                                                            (((~) @ (
13.13/2.53	                                                              ((!!) @ (
13.13/2.53	                                                               ^[Y3 : term]:
13.13/2.53	                                                                 (((Y0 @ 
13.13/2.53	                                                                   (sub @ 
13.13/2.53	                                                                    Y2 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    push @ 
13.13/2.53	                                                                    Y3 @ id))) |
13.13/2.53	                                                                   ((
13.13/2.53	                                                                   (~) @ (
13.13/2.53	                                                                   Y0 @ Y3))))))))))))))))) | 
13.13/2.53	                                      (Y0 @ Y1) | 
13.13/2.53	                                      (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                          (((!!) @ (^[Y3 : term]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    ap @ 
13.13/2.53	                                                                    Y2 @ Y3)) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ Y3))) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ Y2))))))))))))) | 
13.13/2.53	                                      (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                          (((((~) @ (
13.13/2.53	                                                              var @ Y2))) |
13.13/2.53	                                                            (Y0 @ Y2)))))))))))))))) =>
13.13/2.53	            (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.53	                          (((!!) @ (^[Y1 : term]:
13.13/2.53	                                      (((!!) @ (^[Y2 : term]:
13.13/2.53	                                                  (((((~) @ (((!!) @ (
13.13/2.53	                                                              ^[Y3 : subst]:
13.13/2.53	                                                                (((!!) @ (
13.13/2.53	                                                                  ^[Y4 : term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y5 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (!!) @ (
13.13/2.53	                                                                    ^[Y6 : subst]:
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    ((
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y3 @ Y6) @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    sub @ 
13.13/2.53	                                                                    Y4 @ Y6) @ 
13.13/2.53	                                                                    Y5))) |
13.13/2.53	                                                                    (Y0 @ 
13.13/2.53	                                                                    Y3 @ 
13.13/2.53	                                                                    Y4 @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    comp @ 
13.13/2.53	                                                                    Y6 @ Y5)))))))))))))))))) | 
13.13/2.53	                                                    (((~) @ (((!!) @ (
13.13/2.53	                                                              ^[Y3 : term]:
13.13/2.53	                                                                (((!!) @ (
13.13/2.53	                                                                  ^[Y4 : term]:
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (
13.13/2.53	                                                                    (~) @ (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    Y4 @ id))) | 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    Y0 @ 
13.13/2.53	                                                                    id @ 
13.13/2.53	                                                                    (
13.13/2.53	                                                                    ap @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y3 @ id) @ 
13.13/2.54	                                                                    Y4) @ id) | 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    Y3 @ id))))))))))))) | 
13.13/2.54	                                                    (((~) @ (Y0 @ id @ Y1 @ 
13.13/2.54	                                                             id))) | 
13.13/2.54	                                                    (((~) @ (Y0 @ id @ Y2 @ 
13.13/2.54	                                                             id))) | 
13.13/2.54	                                                    (Y0 @ id @ 
13.13/2.54	                                                     (ap @ Y1 @ Y2) @ id) | 
13.13/2.54	                                                    (((~) @ (((!!) @ (
13.13/2.54	                                                              ^[Y3 : subst]:
13.13/2.54	                                                                (((!!) @ (
13.13/2.54	                                                                  ^[Y4 : term]:
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y5 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y6 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    Y3 @ 
13.13/2.54	                                                                    Y4 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y6 @ Y5)))) |
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y3 @ Y6) @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y4 @ Y6) @ 
13.13/2.54	                                                                    Y5)))))))))))))))))))))))))))) =>
13.13/2.54	              (((((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.54	                            (((!!) @ (^[Y1 : term]:
13.13/2.54	                                        (((((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.54	                                                              (((!!) @ (
13.13/2.54	                                                                ^[Y3 : term]:
13.13/2.54	                                                                  (((!!) @ (
13.13/2.54	                                                                    ^[Y4 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y5 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y2 @ Y5) @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y3 @ Y5) @ 
13.13/2.54	                                                                    Y4) |
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    Y3 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y5 @ Y4)))))))))))))))))))) | 
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.54	                                                              (((!!) @ (
13.13/2.54	                                                                ^[Y3 : term]:
13.13/2.54	                                                                  (((!!) @ (
13.13/2.54	                                                                    ^[Y4 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y5 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y2 @ Y5) @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y3 @ Y5) @ 
13.13/2.54	                                                                    Y4))) |
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    Y3 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y5 @ Y4)))))))))))))))))) | 
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.54	                                                              (((Y0 @ id @ 
13.13/2.54	                                                                (sub @ Y1 @ 
13.13/2.54	                                                                 (push @ 
13.13/2.54	                                                                  Y2 @ id)) @ 
13.13/2.54	                                                                id) |
13.13/2.54	                                                                (((~) @ (
13.13/2.54	                                                                  Y0 @ id @ 
13.13/2.54	                                                                  Y2 @ id)))))))))) | 
13.13/2.54	                                          (Y0 @ id @ (lam @ Y1) @ id) | 
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : subst > 
13.13/2.54	                                                                   term > term]:
13.13/2.54	                                                              (((((~) @ (
13.13/2.54	                                                                  ((!!) @ (
13.13/2.54	                                                                   ^[Y3 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y4 : term]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y5 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (sub @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    Y3 @ Y4) @ 
13.13/2.54	                                                                    Y5) =
13.13/2.54	                                                                    (Y2 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y3 @ Y5) @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y4 @ Y5))))))))))))))) | 
13.13/2.54	                                                                (((~) @ (
13.13/2.54	                                                                  ((!!) @ (
13.13/2.54	                                                                   ^[Y3 : term]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    id @ Y3) @ 
13.13/2.54	                                                                    id) |
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    Y3 @ id)))))))))) | 
13.13/2.54	                                                                (Y0 @ id @ 
13.13/2.54	                                                                 (lam @ 
13.13/2.54	                                                                  (Y2 @ sh @ 
13.13/2.54	                                                                   one)) @ 
13.13/2.54	                                                                 id)))))))))))))))) =>
13.13/2.54	                (((!!) @ (^[Y0 : subst > term > subst > $o]:
13.13/2.54	                            (((!!) @ (^[Y1 : term]:
13.13/2.54	                                        (((((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.54	                                                              (((!!) @ (
13.13/2.54	                                                                ^[Y3 : term]:
13.13/2.54	                                                                  (((!!) @ (
13.13/2.54	                                                                    ^[Y4 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y5 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y2 @ Y5) @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y3 @ Y5) @ 
13.13/2.54	                                                                    Y4) |
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    Y3 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y5 @ Y4)))))))))))))))))))) | 
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : subst]:
13.13/2.54	                                                              (((!!) @ (
13.13/2.54	                                                                ^[Y3 : term]:
13.13/2.54	                                                                  (((!!) @ (
13.13/2.54	                                                                    ^[Y4 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y5 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y2 @ Y5) @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y3 @ Y5) @ 
13.13/2.54	                                                                    Y4))) |
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    Y3 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y5 @ Y4)))))))))))))))))) | 
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.54	                                                              (((!!) @ (
13.13/2.54	                                                                ^[Y3 : term]:
13.13/2.54	                                                                  (((
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    Y2 @ id))) | 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    ap @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y2 @ id) @ 
13.13/2.54	                                                                    Y3) @ id) | 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    Y3 @ id))))))))))))) | 
13.13/2.54	                                          (Y0 @ id @ Y1 @ id) | 
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : subst > 
13.13/2.54	                                                                   term > term]:
13.13/2.54	                                                              (((((~) @ (
13.13/2.54	                                                                  ((!!) @ (
13.13/2.54	                                                                   ^[Y3 : term]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    Y3 @ id))) |
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    id @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    id @ Y3) @ 
13.13/2.54	                                                                    id)))))))) | 
13.13/2.54	                                                                (Y0 @ id @ 
13.13/2.54	                                                                 (lam @ 
13.13/2.54	                                                                  (Y2 @ sh @ 
13.13/2.54	                                                                   one)) @ 
13.13/2.54	                                                                 id) | 
13.13/2.54	                                                                (((~) @ (
13.13/2.54	                                                                  ((!!) @ (
13.13/2.54	                                                                   ^[Y3 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y4 : term]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y5 : subst]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (sub @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    Y2 @ 
13.13/2.54	                                                                    Y3 @ Y4) @ 
13.13/2.54	                                                                    Y5) =
13.13/2.54	                                                                    (Y2 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    comp @ 
13.13/2.54	                                                                    Y3 @ Y5) @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y4 @ Y5)))))))))))))))))))))) | 
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.54	                                                              (((((~) @ (
13.13/2.54	                                                                  var @ 
13.13/2.54	                                                                  (sub @ 
13.13/2.54	                                                                   Y2 @ id)))) |
13.13/2.54	                                                                (Y0 @ id @ 
13.13/2.54	                                                                Y2 @ id)))))))))))))))))))))) <=>
13.13/2.54	          (hoasinduction_lthm))) & 
13.13/2.54	        (((hoasinduction_lem3v2_f_lthm) <=>
13.13/2.54	          (((!!) @ (^[Y0 : term]:
13.13/2.54	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.54	                                                              (((!!) @ (
13.13/2.54	                                                                ^[Y3 : subst]:
13.13/2.54	                                                                  (((sub @ 
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    push @ 
13.13/2.54	                                                                    Y2 @ Y3)) =
13.13/2.54	                                                                    (Y1 @ 
13.13/2.54	                                                                    Y3 @ Y2))))))))))))))))))))) & 
13.13/2.54	        hoasinduction_lem3v2_gthm & (((~) @ ulamvar1)) & 
13.13/2.54	        (((hoasapinj1) <=>
13.13/2.54	          (((!!) @ (^[Y0 : term]:
13.13/2.54	                      (((!!) @ (^[Y1 : term]:
13.13/2.54	                                  (((!!) @ (^[Y2 : term]:
13.13/2.54	                                              (((!!) @ (^[Y3 : term]:
13.13/2.54	                                                          (((((ap @ 
13.13/2.54	                                                              (sub @ Y0 @ id) @ 
13.13/2.54	                                                              Y2) != (ap @ 
13.13/2.54	                                                              (sub @ Y1 @ id) @ 
13.13/2.54	                                                              Y3))) |
13.13/2.54	                                                            (((Y0) = (Y1))))))))))))))))))) & 
13.13/2.54	        hoasapnotvar_gthm & axvarshift & 
13.13/2.54	        (((((!!) @ (^[Y0 : term]:
13.13/2.54	                      (((~) @ (((!!) @ (^[Y1 : subst > term > term]:
13.13/2.54	                                          (((~) @ (((!!) @ (^[Y2 : term]:
13.13/2.54	                                                              (((!!) @ (
13.13/2.54	                                                                ^[Y3 : subst]:
13.13/2.54	                                                                  (((sub @ 
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    push @ 
13.13/2.54	                                                                    Y2 @ Y3)) =
13.13/2.54	                                                                    (Y1 @ 
13.13/2.54	                                                                    Y3 @ Y2))))))))))))))))))) <=>
13.13/2.54	          (hoasinduction_lem3v2_f))) & 
13.13/2.54	        (((induction2lem) <=>
13.13/2.54	          (((!!) @ (^[Y0 : term > $o]:
13.13/2.54	                      (((!!) @ (^[Y1 : term]:
13.13/2.54	                                  (((!!) @ (^[Y2 : subst]:
13.13/2.54	                                              (((((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y4 : term]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (
13.13/2.54	                                                                    Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    ap @ 
13.13/2.54	                                                                    Y3 @ Y4)) | 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ Y4))) | 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ Y3))))))))))))) | 
13.13/2.54	                                                (Y0 @ (sub @ Y1 @ Y2)) | 
13.13/2.54	                                                (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    var @ Y3))) |
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y3 @ Y2))))))))) | 
13.13/2.54	                                                (((~) @ (((!!) @ (^[Y3 : term]:
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    (
13.13/2.54	                                                                    (!!) @ (
13.13/2.54	                                                                    ^[Y4 : term]:
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    ((
13.13/2.54	                                                                    (~) @ (
13.13/2.54	                                                                    Y0 @ Y4))) |
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    sub @ 
13.13/2.54	                                                                    Y3 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    push @ 
13.13/2.54	                                                                    Y4 @ id)))))))))) |
13.13/2.54	                                                                    (Y0 @ 
13.13/2.54	                                                                    (
13.13/2.54	                                                                    lam @ Y3)))))))))))))))))))))) & 
13.13/2.54	        hoasinduction_lem1v2_gthm & pushprop_lem0_gthm & 
13.13/2.54	        (((~) @ (var @ (d2term @ d_one)))) & 
13.13/2.54	        (((hoasinduction_p_and_p_prime) =
13.13/2.54	          ((^[Y0 : subst > term > subst > $o,Y1 : term > $o]:
13.13/2.54	              (((!!) @ (^[Y2 : term]: (((Y1 @ Y2) <=> (Y0 @ id @ Y2 @ id)))))))))) & 
13.13/2.54	        (((hoaslam) =
13.13/2.54	          ((^[Y0 : subst,Y1 : subst > term > term]: (d2term @ d_one))))) & 
13.13/2.54	        (((push @ (d2term @ d_one) @ (d2subst @ d_id)) = (d2subst @ d_id))) & 
13.13/2.54	        (((sh) = (d2subst @ d_id))) & 
13.13/2.54	        (((lam @ (d2term @ d_one)) = (d2term @ d_one))) & 
13.13/2.54	        (((one) = (d2term @ d_one))) & 
13.13/2.54	        (((!!) @ (^[Y0 : d_term]: (((Y0) = (d_one))))))))),
13.13/2.54	    inference('simplify boolean subterms', [status(thm)], [zip_derived_cl0])).
13.13/2.54	thf(zip_derived_cl101, plain, ( (axclos)),
13.13/2.54	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])).
13.13/2.54	thf(zip_derived_cl216, plain,
13.13/2.54	    (~ (((!!) @ (^[Y0 : term]:
13.13/2.54	                   (((!!) @ (^[Y1 : subst]:
13.13/2.54	                               (((!!) @ (^[Y2 : subst]:
13.13/2.54	                                           (((sub @ (sub @ Y0 @ Y1) @ Y2) =
13.13/2.54	                                             (sub @ Y0 @ (comp @ Y1 @ Y2)))))))))))))),
13.13/2.54	    inference('demod', [status(thm)], [zip_derived_cl1, zip_derived_cl101])).
13.13/2.54	thf(zip_derived_cl232, plain,
13.13/2.54	    (~ (((!!) @ (^[Y0 : subst]:
13.13/2.54	                   (((!!) @ (^[Y1 : subst]:
13.13/2.54	                               (((sub @ (sub @ '#sk3' @ Y0) @ Y1) = (sub @ 
13.13/2.54	                                 '#sk3' @ (comp @ Y0 @ Y1))))))))))),
13.13/2.54	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl216])).
13.13/2.54	thf(zip_derived_cl233, plain,
13.13/2.54	    (~ (((!!) @ (^[Y0 : subst]:
13.13/2.54	                   (((sub @ (sub @ '#sk3' @ '#sk4') @ Y0) = (sub @ '#sk3' @ 
13.13/2.54	                     (comp @ '#sk4' @ Y0)))))))),
13.13/2.54	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl232])).
13.13/2.54	thf(zip_derived_cl234, plain,
13.13/2.54	    (~ (((sub @ (sub @ '#sk3' @ '#sk4') @ '#sk5') = (sub @ '#sk3' @ 
13.13/2.54	         (comp @ '#sk4' @ '#sk5'))))),
13.13/2.54	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl233])).
13.13/2.54	thf(zip_derived_cl235, plain,
13.13/2.54	    (((sub @ (sub @ '#sk3' @ '#sk4') @ '#sk5')
13.13/2.54	       != (sub @ '#sk3' @ (comp @ '#sk4' @ '#sk5')))),
13.13/2.54	    inference('simplify nested equalities', [status(thm)],
13.13/2.54	              [zip_derived_cl234])).
13.13/2.54	thf(zip_derived_cl3, plain,
13.13/2.54	    ( (((!!) @ (^[Y0 : term]:
13.13/2.54	                  (((??) @ (^[Y1 : d_term]: (((Y0) = (d2term @ Y1)))))))))),
13.13/2.54	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])).
13.13/2.54	thf(zip_derived_cl131, plain,
13.13/2.54	    (![X2 : term]:  (((??) @ (^[Y0 : d_term]: (((X2) = (d2term @ Y0))))))),
13.13/2.54	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3])).
13.13/2.54	thf(zip_derived_cl204, plain,
13.13/2.54	    (![X2 : term]:  (((X2) = (d2term @ ('#sk1' @ X2))))),
13.13/2.54	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl131])).
13.13/2.54	thf(zip_derived_cl210, plain,
13.13/2.54	    (![X2 : term]: ((X2) = (d2term @ ('#sk1' @ X2)))),
13.13/2.54	    inference('simplify nested equalities', [status(thm)],
13.13/2.54	              [zip_derived_cl204])).
13.13/2.54	thf(zip_derived_cl130, plain,
13.13/2.54	    ( (((!!) @ (^[Y0 : d_term]: (((Y0) = (d_one))))))),
13.13/2.54	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])).
13.13/2.54	thf(zip_derived_cl203, plain, (![X2 : d_term]:  (((X2) = (d_one)))),
13.13/2.54	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl130])).
13.13/2.54	thf(zip_derived_cl209, plain, (![X2 : d_term]: ((X2) = (d_one))),
13.13/2.54	    inference('simplify nested equalities', [status(thm)],
13.13/2.54	              [zip_derived_cl203])).
13.13/2.54	thf(zip_derived_cl129, plain, ( (((one) = (d2term @ d_one)))),
13.13/2.54	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])).
13.13/2.54	thf(zip_derived_cl202, plain, (((one) = (d2term @ d_one))),
13.13/2.54	    inference('simplify nested equalities', [status(thm)],
13.13/2.54	              [zip_derived_cl129])).
13.13/2.54	thf(zip_derived_cl222, plain, (![X2 : term]: ((X2) = (one))),
13.13/2.54	    inference('demod', [status(thm)],
13.13/2.54	              [zip_derived_cl210, zip_derived_cl209, zip_derived_cl202])).
13.13/2.54	thf(zip_derived_cl222, plain, (![X2 : term]: ((X2) = (one))),
13.13/2.54	    inference('demod', [status(thm)],
13.13/2.54	              [zip_derived_cl210, zip_derived_cl209, zip_derived_cl202])).
13.13/2.54	thf(zip_derived_cl5, plain,
13.13/2.54	    ( (((!!) @ (^[Y0 : subst]:
13.13/2.54	                  (((??) @ (^[Y1 : d_subst]: (((Y0) = (d2subst @ Y1)))))))))),
13.13/2.54	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])).
13.13/2.54	thf(zip_derived_cl133, plain,
13.13/2.54	    (![X2 : subst]:  (((??) @ (^[Y0 : d_subst]: (((X2) = (d2subst @ Y0))))))),
13.13/2.54	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl5])).
13.13/2.54	thf(zip_derived_cl206, plain,
13.13/2.54	    (![X2 : subst]:  (((X2) = (d2subst @ ('#sk2' @ X2))))),
13.13/2.54	    inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl133])).
13.13/2.54	thf(zip_derived_cl212, plain,
13.13/2.54	    (![X2 : subst]: ((X2) = (d2subst @ ('#sk2' @ X2)))),
13.13/2.54	    inference('simplify nested equalities', [status(thm)],
13.13/2.54	              [zip_derived_cl206])).
13.13/2.54	thf(zip_derived_cl6, plain,
13.13/2.54	    ( (((!!) @ (^[Y0 : d_subst]: (((Y0) = (d_id))))))),
13.13/2.54	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])).
13.13/2.54	thf(zip_derived_cl134, plain, (![X2 : d_subst]:  (((X2) = (d_id)))),
13.13/2.54	    inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl6])).
13.13/2.54	thf(zip_derived_cl207, plain, (![X2 : d_subst]: ((X2) = (d_id))),
13.13/2.54	    inference('simplify nested equalities', [status(thm)],
13.13/2.54	              [zip_derived_cl134])).
13.13/2.54	thf(zip_derived_cl10, plain, ( (((id) = (d2subst @ d_id)))),
13.13/2.54	    inference('lazy_cnf_and', [status(thm)], [zip_derived_cl2])).
13.13/2.54	thf(zip_derived_cl138, plain, (((id) = (d2subst @ d_id))),
13.13/2.54	    inference('simplify nested equalities', [status(thm)], [zip_derived_cl10])).
13.13/2.54	thf(zip_derived_cl225, plain, (![X2 : subst]: ((X2) = (id))),
13.13/2.54	    inference('demod', [status(thm)],
13.13/2.54	              [zip_derived_cl212, zip_derived_cl207, zip_derived_cl138])).
13.13/2.54	thf(zip_derived_cl222, plain, (![X2 : term]: ((X2) = (one))),
13.13/2.54	    inference('demod', [status(thm)],
13.13/2.54	              [zip_derived_cl210, zip_derived_cl209, zip_derived_cl202])).
13.13/2.54	thf(zip_derived_cl236, plain, (((one) != (one))),
13.13/2.54	    inference('demod', [status(thm)],
13.13/2.54	              [zip_derived_cl235, zip_derived_cl222, zip_derived_cl222, 
13.13/2.54	               zip_derived_cl225, zip_derived_cl222])).
13.13/2.54	thf(zip_derived_cl237, plain, ($false),
13.13/2.54	    inference('simplify', [status(thm)], [zip_derived_cl236])).
13.13/2.54	
13.13/2.54	% SZS output end Refutation
13.13/2.54	
13.13/2.54	
13.13/2.54	% /export/starexec/sandbox2/solver/bin/lams/35_full_unif.sh running for 56s
13.13/2.54	% Terminating...
3.82/2.65	% Runner terminated.
3.87/2.72	% Zipperpin 1.5 exiting
3.87/2.75	EOF