TSTP Solution File: SEU558^2 by cocATP---0.2.0
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- Process Solution
%------------------------------------------------------------------------------
% File : cocATP---0.2.0
% Problem : SEU558^2 : TPTP v6.1.0. Bugfixed v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n090.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 13:32:27 EDT 2014
% Result : Timeout 300.03s
% Output : None
% Verified :
% SZS Type : None (Parsing solution fails)
% Syntax : Number of formulae : 0
% Comments :
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem : SEU558^2 : TPTP v6.1.0. Bugfixed v4.0.0.
% % Command : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n090.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 10:42:41 CDT 2014
% % CPUTime : 300.03
% 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 0x26e41b8>, <kernel.DependentProduct object at 0x26e4ab8>) of role type named in_type
% Using role type
% Declaring in:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x217eb48>, <kernel.DependentProduct object at 0x26e4098>) of role type named dsetconstr_type
% Using role type
% Declaring dsetconstr:(fofType->((fofType->Prop)->fofType))
% FOF formula (<kernel.Constant object at 0x26e4518>, <kernel.Sort object at 0x217d128>) 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 0x2177b00>, <kernel.Sort object at 0x217d128>) 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 0x26e4d88>, <kernel.Sort object at 0x217d128>) 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 0x26e41b8>, <kernel.Sort object at 0x217d128>) 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 (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))))))))) of role conjecture named dsetconstr__Cong
% Conjecture to prove = (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))))))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))))))))))']
% Parameter fofType:Type.
% Parameter in:(fofType->(fofType->Prop)).
% 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.
% Trying to prove (dsetconstrI->(dsetconstrEL->(dsetconstrER->(setext->(forall (A:fofType) (B:fofType), ((((eq fofType) A) B)->(forall (Xphi:(fofType->Prop)) (Xpsi:(fofType->Prop)), ((forall (Xx:fofType), (((in Xx) A)->(forall (Xy:fofType), (((in Xy) B)->((((eq fofType) Xx) Xy)->((iff (Xphi Xx)) (Xpsi Xy)))))))->(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi 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_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) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi 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 x30:=(x3 (fun (x5:fofType)=> (P ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))):((P ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (x3 (fun (x5:fofType)=> (P ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))) as proof of (P0 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (x3 (fun (x5:fofType)=> (P ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))) as proof of (P0 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi 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 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xphi Xx)))->(P (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (eq_ref00 P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) P) as proof of (P0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% 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 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% 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 eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> (Xphi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) (fun (x:fofType)=> (Xphi x)))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% 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 eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xphi Xx)))->(P (fun (x:fofType)=> (Xphi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xphi Xx)))->(P (fun (x:fofType)=> (Xphi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xphi Xx)))->(P (fun (Xx:fofType)=> (Xphi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> (Xphi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) (fun (x:fofType)=> (Xphi x)))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xphi Xx)))->(P (fun (x:fofType)=> (Xphi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xphi Xx)))->(P (fun (x:fofType)=> (Xphi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (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 (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 (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 (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% 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 (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% 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 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi 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 x50:((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found x50 as proof of (P ((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 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% 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 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% 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 x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x5 as proof of (P0 A0)
% Found x000:=(x00 Xpsi):(forall (Xx:fofType), (((in Xx) ((dsetconstr B) (fun (Xy:fofType)=> (Xpsi Xy))))->((in Xx) B)))
% Found (x00 Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 B) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 B) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 B) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) 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)=> (Xphi Xx)))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) 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)=> (Xphi Xx)))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found x5:((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x5 as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Found x50:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x50 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x5 as proof of (P0 b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found x30:=(x3 (fun (x6:fofType)=> ((in Xx) A0))):(((in Xx) A0)->((in Xx) A0))
% Found (x3 (fun (x6:fofType)=> ((in Xx) A0))) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (x3 (fun (x6:fofType)=> ((in Xx) A0))) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (fun (Xx:fofType)=> (x3 (fun (x6:fofType)=> ((in Xx) A0)))) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (fun (Xx:fofType)=> (x3 (fun (x6:fofType)=> ((in Xx) A0)))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:fofType)=> (Xpsi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) (fun (x:fofType)=> (Xpsi x)))
% Found (eta_expansion00 (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) 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)=> (Xphi Xx)))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) 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)=> (Xphi Xx)))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xphi Xx)))
% Found eq_ref00:=(eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) b)
% 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 (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found x50:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x50 as proof of (P0 A0)
% Found x000:=(x00 Xpsi):(forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xpsi Xy))))->((in Xx) A)))
% Found (x00 Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% 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 (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x5 as proof of (P0 A0)
% Found x000:=(x00 Xpsi):(forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xpsi Xy))))->((in Xx) A)))
% Found (x00 Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))):fofType
% Found x5 as proof of (P0 A0)
% Found x000:=(x00 Xpsi):(forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xpsi Xy))))->((in Xx) A)))
% Found (x00 Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xpsi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))->((in Xx) A0)))
% 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 (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found eq_ref000:=(eq_ref00 P):((P (Xphi x5))->(P (Xphi x5)))
% Found (eq_ref00 P) as proof of (P0 (Xphi x5))
% Found ((eq_ref0 (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found eq_ref000:=(eq_ref00 P):((P (Xphi x5))->(P (Xphi x5)))
% Found (eq_ref00 P) as proof of (P0 (Xphi x5))
% Found ((eq_ref0 (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% 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 (Xx0:fofType)=> (Xphi Xx0))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx0:fofType)=> (Xphi Xx0))))
% Found eq_ref00:=(eq_ref0 (Xphi x5)):(((eq Prop) (Xphi x5)) (Xphi x5))
% Found (eq_ref0 (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found eq_ref00:=(eq_ref0 (Xphi x5)):(((eq Prop) (Xphi x5)) (Xphi x5))
% Found (eq_ref0 (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% 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) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi 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) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eq_ref000:=(eq_ref00 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref00 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref0 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eq_ref (fofType->Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P):((P (fun (Xx:fofType)=> (Xpsi Xx)))->(P (fun (x:fofType)=> (Xpsi x))))
% Found (eta_expansion_dep000 P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xpsi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) A0)->((in Xx) A0))
% Found (eq_ref00 (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found ((eq_ref0 A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A0) (in Xx))) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A0) (in Xx))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) A0)->((in Xx) A0))
% Found (eq_ref00 (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found ((eq_ref0 A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A0) (in Xx))) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A0) (in Xx))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))))
% Found eq_ref000:=(eq_ref00 P):((P (Xphi x5))->(P (Xphi x5)))
% Found (eq_ref00 P) as proof of (P0 (Xphi x5))
% Found ((eq_ref0 (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found x5:(P ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Instantiate: b:=((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))):fofType
% Found x5 as proof of (P0 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_ref000:=(eq_ref00 P):((P (Xphi x5))->(P (Xphi x5)))
% Found (eq_ref00 P) as proof of (P0 (Xphi x5))
% Found ((eq_ref0 (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found (((eq_ref Prop) (Xphi x5)) P) as proof of (P0 (Xphi x5))
% Found x6:((in Xx) A0)
% Instantiate: A0:=((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))):fofType
% Found (fun (x6:((in Xx) A0))=> x6) as proof of ((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (fun (Xx:fofType) (x6:((in Xx) A0))=> x6) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))))
% Found eq_ref00:=(eq_ref0 (Xphi x5)):(((eq Prop) (Xphi x5)) (Xphi x5))
% Found (eq_ref0 (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found eq_ref00:=(eq_ref0 (Xphi x5)):(((eq Prop) (Xphi x5)) (Xphi x5))
% Found (eq_ref0 (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found ((eq_ref Prop) (Xphi x5)) as proof of (((eq Prop) (Xphi x5)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (Xpsi x5))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: a:=(fun (Xx:fofType)=> (Xphi Xx)):(fofType->Prop)
% Found x5 as proof of (P0 ((dsetconstr A) a))
% Found (x30 x5) as proof of (P0 ((dsetconstr B) a))
% Found ((x3 (fun (x7:fofType)=> (P0 ((dsetconstr x7) a)))) x5) as proof of (P0 ((dsetconstr B) a))
% Found ((x3 (fun (x7:fofType)=> (P0 ((dsetconstr x7) a)))) x5) as proof of (P0 ((dsetconstr B) a))
% 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) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi 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) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi 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)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi 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) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi 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 x50:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: a:=(fun (Xx:fofType)=> (Xphi Xx)):(fofType->Prop)
% Found x50 as proof of (P0 ((dsetconstr A) a))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: a:=(fun (Xx:fofType)=> (Xphi Xx)):(fofType->Prop)
% Found x5 as proof of (P0 ((dsetconstr A) a))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))
% Instantiate: a:=(fun (Xx:fofType)=> (Xphi Xx)):(fofType->Prop)
% Found x5 as proof of (P0 ((dsetconstr A) a))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found x30:=(x3 (fun (x5:fofType)=> (P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))):((P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))->(P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (x3 (fun (x5:fofType)=> (P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))) as proof of (P2 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (x3 (fun (x5:fofType)=> (P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))) as proof of (P2 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found x30:=(x3 (fun (x5:fofType)=> (P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))):((P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))->(P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))
% Found (x3 (fun (x5:fofType)=> (P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))) as proof of (P2 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (x3 (fun (x5:fofType)=> (P1 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx)))))) as proof of (P2 ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found ((eq_ref fofType) b) as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))):(((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (eq_ref0 ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx)))) b)
% Found x5:(P ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Instantiate: A0:=((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))):fofType
% Found x5 as proof of (P0 A0)
% Found x000:=(x00 Xphi):(forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xy:fofType)=> (Xphi Xy))))->((in Xx) A)))
% Found (x00 Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found ((x0 A) Xphi) as proof of (forall (Xx:fofType), (((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))->((in Xx) A0)))
% Found x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))):fofType
% Found x5 as proof of (P0 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 x5:(P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Instantiate: b:=((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))):fofType
% Found x5 as proof of (P0 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 x30:=(x3 (fun (x5:fofType)=> (P b))):((P b)->(P b))
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found (x3 (fun (x5:fofType)=> (P b))) as proof of (P0 b)
% Found eta_expansion0000:=(eta_expansion000 P):((P (fun (Xx:fofType)=> (Xphi Xx)))->(P (fun (x:fofType)=> (Xphi x))))
% Found (eta_expansion000 P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((eta_expansion00 (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> (Xphi Xx))) P) as proof of (P0 (fun (Xx:fofType)=> (Xphi Xx)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> (Xphi Xx))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) (fun (x:fofType)=> (Xphi x)))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> (Xphi Xx))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> (Xphi Xx))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> (Xpsi Xx)))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% 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 (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)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found ((eq_ref fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) as proof of (((eq fofType) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))) b0)
% Found eq_ref00:=(eq_ref0 b0):(((eq fofType) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq fofType) b0) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref fofType) b0) as proof of (((eq fofType) b0) ((dsetconstr B) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% 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 (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 (in Xx)):(((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0))))->((in Xx) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))))
% Found (eq_ref00 (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found ((eq_ref0 ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found (((eq_ref fofType) ((dsetconstr A) (fun (Xx0:fofType)=> (Xpsi Xx0)))) (in Xx)) as proof of (P ((dsetconstr A) (fun (Xx:fofType)=> (Xpsi Xx))))
% Found eq_ref000:=(eq_ref00 (in Xx)):(((in Xx) A0)->((in Xx) A0))
% Found (eq_ref00 (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found ((eq_ref0 A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (((eq_ref fofType) A0) (in Xx)) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A0) (in Xx))) as proof of (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx)))))
% Found (fun (Xx:fofType)=> (((eq_ref fofType) A0) (in Xx))) as proof of (forall (Xx:fofType), (((in Xx) A0)->((in Xx) ((dsetconstr A) (fun (Xx:fofType)=> (Xphi Xx))))))
% Found eq_ref000:=(eq_ref00 (
% EOF
%------------------------------------------------------------------------------