%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SYN374^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n115.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 13:38:17 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  : SYN374^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n115.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 09:30:11 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 0x222d710>, <kernel.DependentProduct object at 0x2410a28>) of role type named cP
% Using role type
% Declaring cP:(fofType->Prop)
% FOF formula ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cP Xy)))) of role conjecture named cX2125
% Conjecture to prove = ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cP Xy)))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cP Xy))))']
% Parameter fofType:Type.
% Parameter cP:(fofType->Prop).
% Trying to prove ((iff ((ex fofType) (fun (Xx:fofType)=> (forall (Xy:fofType), ((iff (cP Xx)) (cP Xy)))))) ((iff ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))) (forall (Xy:fofType), (cP Xy))))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found ((iff_sym0 (cP x0)) (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x0)) (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (fun (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((iff (cP x0)) (cP Xy))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of (((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cP x0)) (cP Xy)))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))->(((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cP x0)) (cP Xy))))
% Found (and_rect00 (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found ((and_rect0 ((iff (cP x0)) (cP Xy))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found (((fun (P:Type) (x1:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x1) x)) ((iff (cP x0)) (cP Xy))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found ((iff_sym1 (cP x0)) (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x0)) (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (fun (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((iff (cP x0)) (cP Xy))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of (((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cP x0)) (cP Xy)))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))->(((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cP x0)) (cP Xy))))
% Found (and_rect00 (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found ((and_rect0 ((iff (cP x0)) (cP Xy))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found (((fun (P:Type) (x1:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x1) x)) ((iff (cP x0)) (cP Xy))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((iff_sym0 (cP x0)) (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((iff_sym (cP Xy)) (cP x0)) (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((iff_sym (cP Xy)) (cP x0)) (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x1:(cP x0)
% Instantiate: x0:=Xy:fofType
% Found (fun (x1:(cP x0))=> x1) as proof of (cP Xy)
% Found (fun (x1:(cP x0))=> x1) as proof of ((cP x0)->(cP Xy))
% Found x1:(cP Xy)
% Instantiate: x0:=Xy:fofType
% Found (fun (x1:(cP Xy))=> x1) as proof of (cP x0)
% Found (fun (x1:(cP Xy))=> x1) as proof of ((cP Xy)->(cP x0))
% Found ((conj10 (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((conj1 ((cP Xy)->(cP x0))) (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((((conj ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0))) (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((((conj ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0))) (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (fun (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of (((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0))))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))->(((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))))
% Found (and_rect00 (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((and_rect0 ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((fun (P:Type) (x1:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x1) x)) ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((fun (P:Type) (x1:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x1) x)) ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((iff_sym1 (cP x0)) (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((iff_sym (cP Xy)) (cP x0)) (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((iff_sym (cP Xy)) (cP x0)) (iff_refl (cP Xy))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy)
% Found ((fun (x2:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x2) Xy)) (x1 x00)) as proof of (cP Xy)
% Found ((fun (x2:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x2) Xy)) (x1 x00)) as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x1:(cP x0)
% Instantiate: x0:=Xy:fofType
% Found (fun (x1:(cP x0))=> x1) as proof of (cP Xy)
% Found (fun (x1:(cP x0))=> x1) as proof of ((cP x0)->(cP Xy))
% Found x1:(cP Xy)
% Instantiate: x0:=Xy:fofType
% Found (fun (x1:(cP Xy))=> x1) as proof of (cP x0)
% Found (fun (x1:(cP Xy))=> x1) as proof of ((cP Xy)->(cP x0))
% Found ((conj10 (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((conj1 ((cP Xy)->(cP x0))) (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((((conj ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0))) (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((((conj ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0))) (fun (x1:(cP x0))=> x1)) (fun (x1:(cP Xy))=> x1)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (iff_refl (cP x0)) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (fun (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of (((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0))))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))->(((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))))
% Found (and_rect00 (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found ((and_rect0 ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((fun (P:Type) (x1:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x1) x)) ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found (((fun (P:Type) (x1:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x1) x)) ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((and ((cP x0)->(cP Xy))) ((cP Xy)->(cP x0)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x000:=(x00 x2):(cP x2)
% Found (x00 x2) as proof of (cP x2)
% Found ((x0 x10) x2) as proof of (cP x2)
% Found ((x0 x10) x2) as proof of (cP x2)
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy)
% Found ((fun (x2:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x2) Xy)) (x1 x00)) as proof of (cP Xy)
% Found ((fun (x2:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x2) Xy)) (x1 x00)) as proof of (cP Xy)
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x000:=(x00 x2):(cP x2)
% Found (x00 x2) as proof of (cP x2)
% Found ((x0 x10) x2) as proof of (cP x2)
% Found ((x0 x10) x2) as proof of (cP x2)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy)) (x1 x00)) as proof of (cP Xy)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy)) (x1 x00)) as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (ex_intro000 (x0 x1)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy)) (x1 x00)) as proof of (cP Xy)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy)) (x1 x00)) as proof of (cP Xy)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (ex_intro000 (x0 x1)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (ex_intro000 (x0 x1)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x000:=(x00 x3):(cP x3)
% Found (x00 x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (ex_intro000 (x0 x1)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x10 as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((iff (cP x2)) (cP Xy))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x000:=(x00 x3):(cP x3)
% Found (x00 x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((iff (cP x2)) (cP Xy))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((iff (cP x2)) (cP Xy)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((iff (cP x2)) (cP Xy))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((ex_ind0 ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((iff (cP x2)) (cP Xy))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((iff (cP x2)) (cP Xy))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x3):(cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (ex_intro000 (x0 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x000:=(x00 x3):(cP x3)
% Found (x00 x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((iff (cP x2)) (cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x00:=(x0 x3):(cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (ex_intro000 (x0 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((ex_ind0 ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x12):(forall (Xy:fofType), (cP Xy))
% Found (x0 x12) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x12) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:=(x2 x3):(cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (x2 x3) as proof of (cP x3)
% Found (ex_intro000 (x2 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x3):(cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (ex_intro000 (x0 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x00:=(x0 x10):(forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x10) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x00:=(x0 x12):(forall (Xy:fofType), (cP Xy))
% Found (x0 x12) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x12) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x000:=(x00 x3):(cP x3)
% Found (x00 x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((ex_ind0 ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x00))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x00:=(x0 x3):(cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (x0 x3) as proof of (cP x3)
% Found (ex_intro000 (x0 x3)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x10:=(x1 x00):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x00) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x01 (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found ((fun (x3:((ex fofType) (fun (Xx:fofType)=> (cP Xx))))=> ((x0 x3) Xy0)) (x1 x00)) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((ex_ind0 ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x10:=(x1 x01):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x01) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x00:=(x0 x11):(forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x11) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found x00:=(x0 Xy):(cP Xy)
% Found (x0 Xy) as proof of (cP Xy)
% Found (x0 Xy) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym00 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym0 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x1)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x1)))=> x30) as proof of (((cP Xy0)->(cP x1))->(cP Xy))
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x000:=(x00 x3):(cP x3)
% Found (x00 x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x40) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of ((cP x3)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))))
% Found (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2))) as proof of (forall (x:fofType), ((cP x)->((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))))
% Found (ex_ind00 (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((ex_ind0 ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) x10)) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((fun (P:Prop) (x3:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x3) (x1 x01))) ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))) (fun (x3:fofType) (x4:(cP x3))=> (iff_refl (cP x2)))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x20:=(x2 x5):(cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (ex_intro000 (x2 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 Xy):(cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found (x4 Xy) as proof of (cP Xy)
% Found x20:=(x2 x5):(cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (ex_intro000 (x2 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x40:=(x4 x0):(cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found (x4 x0) as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP Xy)))
% Found x30:(cP x0)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (cP x0)
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP x0))
% Found (fun (x4:((cP x0)->(cP Xy0))) (x5:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP x0)->(cP Xy0))->(((cP Xy0)->(cP x0))->(cP x0)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP x0)
% Found x40 as proof of (cP x0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP x0)
% Found x40 as proof of (cP x0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x0))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found ((iff_sym1 (cP x0)) (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x0)) (iff_refl (cP Xy))) as proof of ((iff (cP x0)) (cP Xy))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x00:=(x0 Xy):(cP Xy)
% Found (x0 Xy) as proof of (cP Xy)
% Found (x0 Xy) as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found (iff_refl (cP x2)) as proof of ((iff (cP x2)) (cP Xy))
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x33:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x33 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP x0)):((iff (cP x0)) (cP x0))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (iff_refl (cP x0)) as proof of ((iff (cP x0)) (cP Xy))
% Found (fun (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((iff (cP x0)) (cP Xy))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of (((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cP x0)) (cP Xy)))
% Found (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0))) as proof of ((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))->(((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->((iff (cP x0)) (cP Xy))))
% Found (and_rect00 (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found ((and_rect0 ((iff (cP x0)) (cP Xy))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found (((fun (P:Type) (x1:((((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))->(((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))->P)))=> (((((and_rect (((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy:fofType), (cP Xy)))) ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))) P) x1) x)) ((iff (cP x0)) (cP Xy))) (fun (x1:(((ex fofType) (fun (Xx:fofType)=> (cP Xx)))->(forall (Xy0:fofType), (cP Xy0)))) (x2:((forall (Xy0:fofType), (cP Xy0))->((ex fofType) (fun (Xx:fofType)=> (cP Xx)))))=> (iff_refl (cP x0)))) as proof of ((iff (cP x0)) (cP Xy))
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x1)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x1)))=> x30) as proof of (((cP Xy0)->(cP x1))->(cP Xy))
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x40 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x3:(cP x2)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP x2))=> x3) as proof of (cP Xy)
% Found (fun (x3:(cP x2))=> x3) as proof of ((cP x2)->(cP Xy))
% Found x3:(cP Xy)
% Instantiate: x2:=Xy:fofType
% Found (fun (x3:(cP Xy))=> x3) as proof of (cP x2)
% Found (fun (x3:(cP Xy))=> x3) as proof of ((cP Xy)->(cP x2))
% Found ((conj10 (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (((conj1 ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found ((((conj ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2))) (fun (x3:(cP x2))=> x3)) (fun (x3:(cP Xy))=> x3)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x00:=(x0 Xy):(cP Xy)
% Found (x0 Xy) as proof of (cP Xy)
% Found (x0 Xy) as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (x3 x6) as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x00:=(x0 x5):(cP x5)
% Found (x0 x5) as proof of (cP x5)
% Found (x0 x5) as proof of (cP x5)
% Found (ex_intro000 (x0 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (x3 x6) as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (x3 x6) as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (ex_intro000 (x0 x1)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x5):(cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (ex_intro000 (x2 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x0):(cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found (x2 x0) as proof of (cP x0)
% Found x20:=(x2 Xy):(cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found (x2 Xy) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x5):(cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (ex_intro000 (x2 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP x1)
% Found x40 as proof of (cP x1)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP x0)
% Found x40 as proof of (cP x0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP x0)
% Found x40 as proof of (cP x0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x4:(cP x3)
% Instantiate: Xy0:=x3:fofType
% Found x4 as proof of (cP Xy0)
% Found x50:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Found x40 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x50 as proof of (cP Xy)
% Found x4:(cP x3)
% Instantiate: Xy0:=x3:fofType
% Found x4 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy0:=x5:fofType
% Found x6 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (fun (x6:(cP x5))=> (x3 x6)) as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x1:fofType
% Found x30 as proof of (cP x1)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (fun (x6:(cP x5))=> (x3 x6)) as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy0:=x5:fofType
% Found x6 as proof of (cP Xy0)
% Found x50:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x6:((cP Xy0)->(cP x0)))=> x50) as proof of (cP Xy)
% Found (fun (x6:((cP Xy0)->(cP x0)))=> x50) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Found x40 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (fun (x6:(cP x5))=> (x3 x6)) as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x50:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x6:((cP Xy0)->(cP x0)))=> x50) as proof of (cP Xy)
% Found (fun (x6:((cP Xy0)->(cP x0)))=> x50) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x1)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x1)))=> x30) as proof of (((cP Xy0)->(cP x1))->(cP Xy))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x6:(cP x5))=> x30) as proof of (cP Xy)
% Found (fun (x6:(cP x5))=> x30) as proof of ((cP x5)->(cP Xy))
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x6:(cP x5))=> x30) as proof of (cP Xy)
% Found (fun (x6:(cP x5))=> x30) as proof of ((cP x5)->(cP Xy))
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Found x40 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (cP Xy)
% Found (fun (x4:((cP Xy0)->(cP x0)))=> x30) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: x5:=Xy:fofType
% Found x20 as proof of (cP x5)
% Found (ex_intro000 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0))) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (fun (x4:(forall (Xy:fofType), (cP Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0)))) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (fun (x4:(forall (Xy:fofType), (cP Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0)))) as proof of ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (fun (x6:(cP x5))=> (x3 x6)) as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x6:(cP x5))=> x30) as proof of (cP Xy)
% Found (fun (x5:fofType) (x6:(cP x5))=> x30) as proof of ((cP x5)->(cP Xy))
% Found (fun (x5:fofType) (x6:(cP x5))=> x30) as proof of (forall (x:fofType), ((cP x)->(cP Xy)))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x5):(cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (ex_intro000 (x2 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: x5:=Xy:fofType
% Found x20 as proof of (cP x5)
% Found (ex_intro000 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0))) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (fun (x4:(forall (Xy:fofType), (cP Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0)))) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (fun (x4:(forall (Xy:fofType), (cP Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0)))) as proof of ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (fun (x6:(cP x5))=> (x3 x6)) as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x21) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x21) as proof of ((cP x5)->(cP Xy0))
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (fun (x6:(cP x5))=> x30) as proof of (cP Xy)
% Found (fun (x5:fofType) (x6:(cP x5))=> x30) as proof of ((cP x5)->(cP Xy))
% Found (fun (x5:fofType) (x6:(cP x5))=> x30) as proof of (forall (x:fofType), ((cP x)->(cP Xy)))
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x32:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x32 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: x5:=Xy:fofType
% Found x20 as proof of (cP x5)
% Found (ex_intro000 x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((ex_intro00 Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (((ex_intro0 (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) x20) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0))) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (fun (x4:(forall (Xy:fofType), (cP Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0)))) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (fun (x4:(forall (Xy:fofType), (cP Xy)))=> ((((ex_intro fofType) (fun (Xx:fofType)=> (cP Xx))) Xy) (x2 (x4 x0)))) as proof of ((forall (Xy:fofType), (cP Xy))->((ex fofType) (fun (Xx:fofType)=> (cP Xx))))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found (x3 x6) as proof of (cP x0)
% Found (fun (x6:(cP x5))=> (x3 x6)) as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:=(x2 x31):(cP Xy)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x21) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x21) as proof of ((cP x5)->(cP Xy0))
% Found x22:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x22 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x10:=(x1 x02):((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found (x1 x02) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found x00:=(x0 x12):(forall (Xy:fofType), (cP Xy))
% Found (x0 x12) as proof of (forall (Xy:fofType), (cP Xy))
% Found (x0 x12) as proof of (forall (Xy:fofType), (cP Xy))
% Found iff_refl0:=(iff_refl (cP x2)):((iff (cP x2)) (cP x2))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found (iff_refl (cP x2)) as proof of ((and ((cP x2)->(cP Xy))) ((cP Xy)->(cP x2)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x21) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x21) as proof of ((cP x5)->(cP Xy0))
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x33:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x33 as proof of (cP Xy)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Found x31 as proof of (cP x0)
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP x0)
% Found x40 as proof of (cP x0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x21) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x21) as proof of ((cP x5)->(cP Xy0))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found iff_refl0:=(iff_refl (cP Xy)):((iff (cP Xy)) (cP Xy))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_refl (cP Xy)) as proof of ((iff (cP Xy)) (cP x2))
% Found (iff_sym10 (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found ((iff_sym1 (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found (((iff_sym (cP Xy)) (cP x2)) (iff_refl (cP Xy))) as proof of ((iff (cP x2)) (cP Xy))
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x20:=(x2 x5):(cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (ex_intro000 (x2 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x41:(cP Xy0)
% Found x41 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Found x21 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x21) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x21) as proof of ((cP x5)->(cP Xy0))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP Xy0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x1:fofType
% Found x30 as proof of (cP x1)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x41) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x30:(cP Xy)
% Instantiate: Xy:=x1:fofType
% Found x30 as proof of (cP x1)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP x1)
% Instantiate: Xy:=x1:fofType
% Found x40 as proof of (cP Xy)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found (fun (x6:(cP x5))=> x6) as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (cP Xy)
% Found (fun (x5:((cP Xy0)->(cP x0)))=> x20) as proof of (((cP Xy0)->(cP x0))->(cP Xy))
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x30:=(x3 x40):(cP Xy0)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x51:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x51 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x51:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x51 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x40 as proof of (cP Xy)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x30 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found x41:(cP Xy0)
% Instantiate: Xy:=Xy0:fofType
% Found x41 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x41:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x41 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x5):(cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (x2 x5) as proof of (cP x5)
% Found (ex_intro000 (x2 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x21) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x21) as proof of ((cP x5)->(cP Xy0))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x000:=(x00 x3):(cP x3)
% Found (x00 x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found ((x0 x10) x3) as proof of (cP x3)
% Found x31:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x31 as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x23:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x23 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x20 as proof of (cP Xy0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x6:(cP x5)
% Instantiate: Xy:=x5:fofType
% Found x6 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x31) as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> (x2 x30)) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found (ex_ind10 (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found ((ex_ind1 (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found (((fun (P:Prop) (x5:(forall (x:fofType), ((cP x)->P)))=> (((((ex_ind fofType) (fun (Xx:fofType)=> (cP Xx))) P) x5) x4)) (cP Xy0)) (fun (x5:fofType) (x6:(cP x5))=> (x2 x30))) as proof of (cP Xy0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x40:(cP Xy0)
% Instantiate: Xy0:=x0:fofType
% Found x40 as proof of (cP x0)
% Found x20:=(x2 x30):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x30) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> (x2 x30)) as proof of ((cP x5)->(cP Xy0))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x50 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy0:=Xy:fofType
% Found x21 as proof of (cP Xy0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x50:(cP x0)
% Found x50 as proof of (cP x0)
% Found x50:(cP x0)
% Instantiate: Xy0:=x0:fofType
% Found x50 as proof of (cP Xy0)
% Found x30:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP x0)
% Found x40:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x40 as proof of (cP Xy)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x20:(cP Xy)
% Found x20 as proof of (cP Xy0)
% Found x30:=(x3 x40):(cP Xy0)
% Instantiate: Xy0:=Xy:fofType
% Found (x3 x40) as proof of (cP Xy)
% Found (x3 x40) as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x20) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x21) as proof of (cP Xy0)
% Found (fun (x5:fofType) (x6:(cP x5))=> x21) as proof of ((cP x5)->(cP Xy0))
% Found (fun (x5:fofType) (x6:(cP x5))=> x21) as proof of (forall (x:fofType), ((cP x)->(cP Xy0)))
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x40:=(x4 x5):(cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (x4 x5) as proof of (cP x5)
% Found (ex_intro000 (x4 x5)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x00:=(x0 x1):(cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (x0 x1) as proof of (cP x1)
% Found (ex_intro000 (x0 x1)) as proof of ((ex fofType) (fun (Xx:fofType)=> (cP Xx)))
% Found x30:(cP x0)
% Found x30 as proof of (cP x0)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x20:=(x2 x30):(cP Xy)
% Found (x2 x30) as proof of (cP Xy0)
% Found (x2 x30) as proof of (cP Xy0)
% Found x31:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x31 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x21 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (fun (x6:(cP x5))=> x20) as proof of (cP Xy0)
% Found (fun (x6:(cP x5))=> x20) as proof of ((cP x5)->(cP Xy0))
% Found x30:(cP x0)
% Instantiate: Xy:=x0:fofType
% Found x30 as proof of (cP Xy)
% Found x21:(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found x21 as proof of (cP Xy0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:(cP Xy)
% Instantiate: Xy:=x0:fofType
% Found x20 as proof of (cP x0)
% Found x20:=(x2 x31):(cP Xy)
% Instantiate: Xy:=Xy0:fofType
% Found (x2 x31) as proof of (cP Xy0)
% Found (x2 x3
% EOF
%------------------------------------------------------------------------------