%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEU637^2 : TPTP v6.1.0. Released v3.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n180.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:32:40 EDT 2014

% Result   : Timeout 300.02s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEU637^2 : TPTP v6.1.0. Released v3.7.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n180.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 10:59:06 CDT 2014
% % CPUTime  : 300.02 
% Python 2.7.5
% Using paths ['/home/cristobal/cocATP/CASC/TPTP/', '/export/starexec/sandbox/benchmark/', '/export/starexec/sandbox/benchmark/']
% FOF formula (<kernel.Constant object at 0x28625f0>, <kernel.DependentProduct object at 0x240df38>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x24283f8>, <kernel.Single object at 0x2862488>) of role type named emptyset_type
% Using role type
% Declaring emptyset:fofType
% FOF formula (<kernel.Constant object at 0x2862d88>, <kernel.DependentProduct object at 0x240dea8>) of role type named setadjoin_type
% Using role type
% Declaring setadjoin:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x2862680>, <kernel.DependentProduct object at 0x240ddd0>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x2862488>, <kernel.Sort object at 0x22edbd8>) of role type named dsetconstrI_type
% Using role type
% Declaring dsetconstrI:Prop
% FOF formula (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))) of role definition named dsetconstrI
% A new definition: (((eq Prop) dsetconstrI) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))))
% Defined: dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy)))))))
% FOF formula (<kernel.Constant object at 0x2862488>, <kernel.Sort object at 0x22edbd8>) of role type named dsetconstrEL_type
% Using role type
% Declaring dsetconstrEL:Prop
% FOF formula (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))) of role definition named dsetconstrEL
% A new definition: (((eq Prop) dsetconstrEL) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))))
% Defined: dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% FOF formula (<kernel.Constant object at 0x2862d88>, <kernel.Sort object at 0x22edbd8>) of role type named dsetconstrER_type
% Using role type
% Declaring dsetconstrER:Prop
% FOF formula (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))) of role definition named dsetconstrER
% A new definition: (((eq Prop) dsetconstrER) (forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))))
% Defined: dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx)))
% FOF formula (<kernel.Constant object at 0x240dcb0>, <kernel.Sort object at 0x22edbd8>) of role type named setext_type
% Using role type
% Declaring setext:Prop
% FOF formula (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))) of role definition named setext
% A new definition: (((eq Prop) setext) (forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))))
% Defined: setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B))))
% FOF formula (<kernel.Constant object at 0x240dfc8>, <kernel.Sort object at 0x22edbd8>) of role type named uniqinunit_type
% Using role type
% Declaring uniqinunit:Prop
% FOF formula (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))) of role definition named uniqinunit
% A new definition: (((eq Prop) uniqinunit) (forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))))
% Defined: uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy)))
% FOF formula (<kernel.Constant object at 0x240df38>, <kernel.Sort object at 0x22edbd8>) of role type named eqinunit_type
% Using role type
% Declaring eqinunit:Prop
% FOF formula (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))) of role definition named eqinunit
% A new definition: (((eq Prop) eqinunit) (forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))))
% Defined: eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset))))
% FOF formula (<kernel.Constant object at 0x240db00>, <kernel.DependentProduct object at 0x240d680>) of role type named singleton_type
% Using role type
% Declaring singleton:(fofType->Prop)
% FOF formula (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))) of role definition named singleton
% A new definition: (((eq (fofType->Prop)) singleton) (fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))))
% Defined: singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset))))))
% FOF formula (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->(singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))))))))) of role conjecture named singletonprop
% Conjecture to prove = (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->(singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))))))))):Prop
% We need to prove ['(dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->(singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% Parameter emptyset:fofType.
% Parameter setadjoin:(fofType->(fofType->fofType)).
% Parameter dsetconstr:(fofType->((fofType->Prop)->fofType)).
% Definition dsetconstrI:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) A)->((Xphi Xx)->((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))):Prop.
% Definition dsetconstrEL:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A))):Prop.
% Definition dsetconstrER:=(forall (A:fofType) (Xphi:(fofType->Prop)) (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->(Xphi Xx))):Prop.
% Definition setext:=(forall (A:fofType) (B:fofType), ((forall (Xx:fofType), (((in Xx) A)->((in Xx) B)))->((forall (Xx:fofType), (((in Xx) B)->((in Xx) A)))->(((eq fofType) A) B)))):Prop.
% Definition uniqinunit:=(forall (Xx:fofType) (Xy:fofType), (((in Xx) ((setadjoin Xy) emptyset))->(((eq fofType) Xx) Xy))):Prop.
% Definition eqinunit:=(forall (Xx:fofType) (Xy:fofType), ((((eq fofType) Xx) Xy)->((in Xx) ((setadjoin Xy) emptyset)))):Prop.
% Definition singleton:=(fun (A:fofType)=> ((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (((eq fofType) A) ((setadjoin Xx) emptyset)))))):(fofType->Prop).
% Trying to prove (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(uniqinunit->(eqinunit->(forall (A:fofType) (Xphi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) A)->((Xphi Xx)->((Xphi Xy)->(((eq fofType) Xx) Xy)))))))->(((ex fofType) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->(singleton ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))))))))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found (eq_ref0 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found x1000:=(x100 x7):(((in x7) A)->((Xphi x7)->((in x7) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))
% Found (x100 x7) as proof of (((in x7) A)->((Xphi x7)->((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found ((x10 Xphi) x7) as proof of (((in x7) A)->((Xphi x7)->((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x7) as proof of (((in x7) A)->((Xphi x7)->((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x7) as proof of (((in x7) A)->((Xphi x7)->((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x7) as proof of (((in x7) A)->((Xphi x7)->((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (and_rect00 (((x A) Xphi) x7)) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((and_rect0 ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x7)) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((fun (P:Type) (x10:(((in x7) A)->((Xphi x7)->P)))=> (((((and_rect ((in x7) A)) (Xphi x7)) P) x10) x8)) ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x7)) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((fun (P:Type) (x10:(((in x7) A)->((Xphi x7)->P)))=> (((((and_rect ((in x7) A)) (Xphi x7)) P) x10) x8)) ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x7)) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x1000:=(x100 x8):(((in x8) A)->((Xphi x8)->((in x8) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))
% Found (x100 x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found ((x10 Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (and_rect00 (((x A) Xphi) x8)) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((and_rect0 ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x8)) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((fun (P:Type) (x10:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x10) x9)) ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x8)) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((fun (P:Type) (x10:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x10) x9)) ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x8)) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset)))))->(P0 (fun (x:fofType)=> ((and ((in x) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin x) emptyset))))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) (fun (x:fofType)=> ((and ((in x) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x) emptyset)))))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset))))) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found x1000:=(x100 x8):(((in x8) A)->((Xphi x8)->((in x8) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))))
% Found (x100 x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found ((x10 Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (((x A) Xphi) x8) as proof of (((in x8) A)->((Xphi x8)->((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found (and_rect00 (((x A) Xphi) x8)) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((and_rect0 ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x8)) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((fun (P:Type) (x10:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x10) x9)) ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x8)) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x9:((and ((in x8) A)) (Xphi x8)))=> (((fun (P:Type) (x10:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x10) x9)) ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((x A) Xphi) x8))) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset)))))->(P0 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eq_ref0 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset)))))->(P0 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eq_ref0 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))) (((eq fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) ((setadjoin Xx) emptyset))))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found x9:((in x7) A)
% Instantiate: x11:=x7:fofType
% Found x9 as proof of ((in x11) A)
% Found x10:(Xphi x7)
% Instantiate: x11:=x7:fofType
% Found x10 as proof of (Xphi x11)
% Found ((x1200 x9) x10) as proof of ((in x11) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((x120 x11) x9) x10) as proof of ((in x11) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((((x12 Xphi) x11) x9) x10) as proof of ((in x11) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x11) x9) x10) as proof of ((in x11) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x11) x9) x10) as proof of ((in x11) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((in x6) A)) (Xphi x6)))->(P0 ((and ((in x6) A)) (Xphi x6))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref0 ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((in x6) A)) (Xphi x6)))->(P0 ((and ((in x6) A)) (Xphi x6))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref0 ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((x40 x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((x4 Xx) x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x10:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) A)) (Xphi x6))):(((eq Prop) ((and ((in x6) A)) (Xphi x6))) ((and ((in x6) A)) (Xphi x6)))
% Found (eq_ref0 ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) A)) (Xphi x6))):(((eq Prop) ((and ((in x6) A)) (Xphi x6))) ((and ((in x6) A)) (Xphi x6)))
% Found (eq_ref0 ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found x11:(Xphi x8)
% Instantiate: x7:=x8:fofType
% Found x11 as proof of (Xphi x7)
% Found x10:((in x8) A)
% Instantiate: x7:=x8:fofType
% Found x10 as proof of ((in x7) A)
% Found ((x1200 x10) x11) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((x120 x7) x10) x11) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((((x12 Xphi) x7) x10) x11) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x7) x10) x11) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x7) x10) x11) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x10:((in x7) A)
% Instantiate: x9:=x7:fofType
% Found x10 as proof of ((in x9) A)
% Found x11:(Xphi x7)
% Instantiate: x9:=x7:fofType
% Found x11 as proof of (Xphi x9)
% Found ((x1200 x10) x11) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((x120 x9) x10) x11) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((((x12 Xphi) x9) x10) x11) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x9) x10) x11) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x9) x10) x11) as proof of ((in x9) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x10:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin Xx) emptyset)))))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found (eq_ref0 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x8:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->(P0 (fun (x:fofType)=> ((and ((in x) A)) (Xphi x)))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))->(P0 (fun (x:fofType)=> ((and ((in x) A)) (Xphi x)))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx)))) P0) as proof of (P1 (fun (Xx:fofType)=> ((and ((in Xx) A)) (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))->(P0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))->(P0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) P0) as proof of (P1 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))):(((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found eq_ref00:=(eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))):(((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))):(((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))):(((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found (eq_ref0 ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found ((eq_ref Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) as proof of (((eq Prop) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x11)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x11)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x11)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x11)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found ((x40 x11) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found (((x4 Xx) x11) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x11) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((x40 x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((x4 Xx) x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x10:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((x40 x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((x4 Xx) x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x10:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((x40 x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((x4 Xx) x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((in x6) A)) (Xphi x6)))->(P0 ((and ((in x6) A)) (Xphi x6))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref0 ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((in x6) A)) (Xphi x6)))->(P0 ((and ((in x6) A)) (Xphi x6))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found ((eq_ref0 ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found (((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) P0) as proof of (P1 ((and ((in x6) A)) (Xphi x6)))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) A)) (Xphi x6))):(((eq Prop) ((and ((in x6) A)) (Xphi x6))) ((and ((in x6) A)) (Xphi x6)))
% Found (eq_ref0 ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) A)) (Xphi x6))):(((eq Prop) ((and ((in x6) A)) (Xphi x6))) ((and ((in x6) A)) (Xphi x6)))
% Found (eq_ref0 ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x9) emptyset))->(P ((setadjoin x9) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x9) emptyset))
% Found ((eq_ref0 ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x9) emptyset))->(P ((setadjoin x9) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x9) emptyset))
% Found ((eq_ref0 ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) A)) (Xphi x6))):(((eq Prop) ((and ((in x6) A)) (Xphi x6))) ((and ((in x6) A)) (Xphi x6)))
% Found (eq_ref0 ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((in x6) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))) (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((setadjoin x6) emptyset))))
% Found eq_ref00:=(eq_ref0 ((and ((in x6) A)) (Xphi x6))):(((eq Prop) ((and ((in x6) A)) (Xphi x6))) ((and ((in x6) A)) (Xphi x6)))
% Found (eq_ref0 ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found ((eq_ref Prop) ((and ((in x6) A)) (Xphi x6))) as proof of (((eq Prop) ((and ((in x6) A)) (Xphi x6))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x7) emptyset))->(P ((setadjoin x7) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x7) emptyset))
% Found ((eq_ref0 ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x7) emptyset))->(P ((setadjoin x7) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x7) emptyset))
% Found ((eq_ref0 ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x9) emptyset))->(P ((setadjoin x9) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x9) emptyset))
% Found ((eq_ref0 ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x8:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x9) emptyset))->(P ((setadjoin x9) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x9) emptyset))
% Found ((eq_ref0 ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) P) as proof of (P0 ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((x40 x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((x4 Xx) x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x12:(Xphi x7))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x11:((in x7) A)) (x12:(Xphi x7))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((Xphi x7)->((in Xx) ((setadjoin x9) emptyset)))
% Found (fun (x11:((in x7) A)) (x12:(Xphi x7))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of (((in x7) A)->((Xphi x7)->((in Xx) ((setadjoin x9) emptyset))))
% Found (and_rect00 (fun (x11:((in x7) A)) (x12:(Xphi x7))=> (((x4 Xx) x9) ((eq_ref fofType) Xx)))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((and_rect0 ((in Xx) ((setadjoin x9) emptyset))) (fun (x11:((in x7) A)) (x12:(Xphi x7))=> (((x4 Xx) x9) ((eq_ref fofType) Xx)))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((fun (P:Type) (x11:(((in x7) A)->((Xphi x7)->P)))=> (((((and_rect ((in x7) A)) (Xphi x7)) P) x11) x8)) ((in Xx) ((setadjoin x9) emptyset))) (fun (x11:((in x7) A)) (x12:(Xphi x7))=> (((x4 Xx) x9) ((eq_ref fofType) Xx)))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x10:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((fun (P:Type) (x11:(((in x7) A)->((Xphi x7)->P)))=> (((((and_rect ((in x7) A)) (Xphi x7)) P) x11) x8)) ((in Xx) ((setadjoin x9) emptyset))) (fun (x11:((in x7) A)) (x12:(Xphi x7))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x12:(Xphi x8))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x11:((in x8) A)) (x12:(Xphi x8))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((Xphi x8)->((in Xx) ((setadjoin x7) emptyset)))
% Found (fun (x11:((in x8) A)) (x12:(Xphi x8))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of (((in x8) A)->((Xphi x8)->((in Xx) ((setadjoin x7) emptyset))))
% Found (and_rect00 (fun (x11:((in x8) A)) (x12:(Xphi x8))=> (((x4 Xx) x7) ((eq_ref fofType) Xx)))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((and_rect0 ((in Xx) ((setadjoin x7) emptyset))) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> (((x4 Xx) x7) ((eq_ref fofType) Xx)))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in Xx) ((setadjoin x7) emptyset))) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> (((x4 Xx) x7) ((eq_ref fofType) Xx)))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x10:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in Xx) ((setadjoin x7) emptyset))) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x11)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x11)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x11)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x11)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found ((x40 x11) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found (((x4 Xx) x11) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x11) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x11) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x7) emptyset))->(P ((setadjoin x7) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x7) emptyset))
% Found ((eq_ref0 ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x7) emptyset))->(P ((setadjoin x7) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x7) emptyset))
% Found ((eq_ref0 ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((setadjoin x9) emptyset))->((in Xx) ((setadjoin x9) emptyset)))
% Found (eq_ref00 (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found ((eq_ref0 ((setadjoin x9) emptyset)) (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x11) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((x40 x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((x4 Xx) x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x10:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((setadjoin x9) emptyset))->((in Xx) ((setadjoin x9) emptyset)))
% Found (eq_ref00 (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found ((eq_ref0 ((setadjoin x9) emptyset)) (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found (((eq_ref fofType) ((setadjoin x9) emptyset)) (in Xx)) as proof of (P ((setadjoin x9) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((setadjoin x7) emptyset))->(P ((setadjoin x7) emptyset)))
% Found (eq_ref00 P) as proof of (P0 ((setadjoin x7) emptyset))
% Found ((eq_ref0 ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) P) as proof of (P0 ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x11:((in x8) A)
% Instantiate: x7:=x8:fofType
% Found (fun (x12:(Xphi x8))=> x11) as proof of ((in x7) A)
% Found (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11) as proof of ((Xphi x8)->((in x7) A))
% Found (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11) as proof of (((in x8) A)->((Xphi x8)->((in x7) A)))
% Found (and_rect00 (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11)) as proof of ((in x7) A)
% Found ((and_rect0 ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11)) as proof of ((in x7) A)
% Found (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11)) as proof of ((in x7) A)
% Found (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11)) as proof of ((in x7) A)
% Found eq_ref000:=(eq_ref00 Xphi):((Xphi x8)->(Xphi x8))
% Found (eq_ref00 Xphi) as proof of ((Xphi x8)->(Xphi x7))
% Found ((eq_ref0 x8) Xphi) as proof of ((Xphi x8)->(Xphi x7))
% Found (((eq_ref fofType) x8) Xphi) as proof of ((Xphi x8)->(Xphi x7))
% Found (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi)) as proof of ((Xphi x8)->(Xphi x7))
% Found (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi)) as proof of (((in x8) A)->((Xphi x8)->(Xphi x7)))
% Found (and_rect00 (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi))) as proof of (Xphi x7)
% Found ((and_rect0 (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi))) as proof of (Xphi x7)
% Found (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi))) as proof of (Xphi x7)
% Found (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi))) as proof of (Xphi x7)
% Found ((x1000 (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11))) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi)))) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((x100 x7) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11))) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi)))) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((((x10 Xphi) x7) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11))) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi)))) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((((x A) Xphi) x7) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11))) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi)))) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x9:((and ((in x8) A)) (Xphi x8)))=> (((((x A) Xphi) x7) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) ((in x7) A)) (fun (x11:((in x8) A)) (x12:(Xphi x8))=> x11))) (((fun (P:Type) (x11:(((in x8) A)->((Xphi x8)->P)))=> (((((and_rect ((in x8) A)) (Xphi x8)) P) x11) x9)) (Xphi x7)) (fun (x11:((in x8) A))=> (((eq_ref fofType) x8) Xphi))))) as proof of ((in x7) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x9) emptyset)):(((eq fofType) ((setadjoin x9) emptyset)) ((setadjoin x9) emptyset))
% Found (eq_ref0 ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (fun (x100:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> x100) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 ((setadjoin x9) emptyset)):(((eq fofType) ((setadjoin x9) emptyset)) ((setadjoin x9) emptyset))
% Found (eq_ref0 ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found ((eq_ref fofType) ((setadjoin x9) emptyset)) as proof of (((eq fofType) ((setadjoin x9) emptyset)) b)
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((setadjoin x7) emptyset))->((in Xx) ((setadjoin x7) emptyset)))
% Found (eq_ref00 (in Xx)) as proof of (P ((setadjoin x7) emptyset))
% Found ((eq_ref0 ((setadjoin x7) emptyset)) (in Xx)) as proof of (P ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) (in Xx)) as proof of (P ((setadjoin x7) emptyset))
% Found (((eq_ref fofType) ((setadjoin x7) emptyset)) (in Xx)) as proof of (P ((setadjoin x7) emptyset))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x7)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found ((x40 x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (((x4 Xx) x7) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x7) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x7) emptyset))
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) x9)
% Found (x400 ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found ((x40 x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (((x4 Xx) x9) ((eq_ref fofType) Xx)) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found (fun (x12:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))=> (((x4 Xx) x9) ((eq_ref fofType) Xx))) as proof of ((in Xx) ((setadjoin x9) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x7) emptyset))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((setadjoin x9) emptyset))
% Found x80:(P ((d
% EOF
%------------------------------------------------------------------------------