TSTP Solution File: SEV380^5 by cocATP---0.2.0

View Problem - Process Solution 
%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV380^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n180.star.cs.uiowa.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2609 0 2.40GHz
% Memory   : 32286.75MB
% OS       : Linux 2.6.32-431.20.3.el6.x86_64
% CPULimit : 300s
% DateTime : Thu Jul 17 13:34:07 EDT 2014

% Result   : Timeout 300.10s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV380^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n180.star.cs.uiowa.edu
% % Model    : x86_64 x86_64
% % CPU      : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz
% % Memory   : 32286.75MB
% % OS       : Linux 2.6.32-431.20.3.el6.x86_64
% % CPULimit : 300
% % DateTime : Thu Jul 17 09:00:46 CDT 2014
% % CPUTime  : 300.10 
% 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 0x29bf8c0>, <kernel.DependentProduct object at 0x276ed40>) of role type named cGVB_APPLY
% Using role type
% Declaring cGVB_APPLY:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x29bfb00>, <kernel.DependentProduct object at 0x276edd0>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x258eea8>, <kernel.DependentProduct object at 0x276ef80>) of role type named cGVB_ITERATE
% Using role type
% Declaring cGVB_ITERATE:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x29bfb00>, <kernel.DependentProduct object at 0x276eb48>) of role type named cGVB_FUNCTION
% Using role type
% Declaring cGVB_FUNCTION:(fofType->Prop)
% FOF formula (forall (Xf:fofType), (((and (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))->((ex fofType) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))))) of role conjecture named cGVB_THM15B_1
% Conjecture to prove = (forall (Xf:fofType), (((and (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))->((ex fofType) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))))):Prop
% Parameter fofType_DUMMY:fofType.
% We need to prove ['(forall (Xf:fofType), (((and (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))->((ex fofType) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))))']
% Parameter fofType:Type.
% Parameter cGVB_APPLY:(fofType->(fofType->fofType)).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_ITERATE:(fofType->(fofType->Prop)).
% Parameter cGVB_FUNCTION:(fofType->Prop).
% Trying to prove (forall (Xf:fofType), (((and (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))->((ex fofType) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 (ex fofType)):(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_FUNCTION x)) ((cGVB_ITERATE Xf) x))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eta_expansion_dep000 (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eta_expansion_dep00 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_FUNCTION x)) ((cGVB_ITERATE Xf) x))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eta_expansion00 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eta_expansion0 Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_FUNCTION x)) ((cGVB_ITERATE Xf) x))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eta_expansion00 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eta_expansion0 Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 (ex fofType)):(((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY x2) x)) x))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x)))))))
% Found (eta_expansion_dep000 (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY x2) x)) x))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x)))))))
% Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY x2) x)) x))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x)))))))
% Found (eta_expansion000 (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eta_expansion00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found (((eta_expansion0 Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: b:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eq_ref00:=(eq_ref0 (f x0)):(((eq Prop) (f x0)) (f x0))
% Found (eq_ref0 (f x0)) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found ((eq_ref Prop) (f x0)) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (((eq Prop) (f x0)) ((and (cGVB_M x0)) (((eq fofType) ((cGVB_APPLY Xf) x0)) x0)))
% Found (fun (x0:fofType)=> ((eq_ref Prop) (f x0))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_FUNCTION x)) ((cGVB_ITERATE Xf) x))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eta_expansion000 (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P b))
% Found ((eta_expansion00 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P b))
% Found (((eta_expansion0 Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P b))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P b))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P b))
% Found (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType))) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P b))
% Found (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType))) as proof of ((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P b)))
% Found (and_rect00 (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P b)
% Found ((and_rect0 (P b)) (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P b)
% Found (((fun (P0:Type) (x0:((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->P0)))=> (((((and_rect (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))) P0) x0) x)) (P b)) (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P b)
% Found (((fun (P0:Type) (x0:((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->P0)))=> (((((and_rect (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))) P0) x0) x)) (P b)) (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P b)
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x2)):(((eq Prop) (f x2)) (f x2))
% Found (eq_ref0 (f x2)) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found ((eq_ref Prop) (f x2)) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (((eq Prop) (f x2)) ((and (cGVB_M x2)) (((eq fofType) ((cGVB_APPLY Xf) x2)) x2)))
% Found (fun (x2:fofType)=> ((eq_ref Prop) (f x2))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eta_expansion0000:=(eta_expansion000 (ex fofType)):(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_FUNCTION x)) ((cGVB_ITERATE Xf) x))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eta_expansion000 (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found ((eta_expansion00 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found (((eta_expansion0 Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType))) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType))) as proof of ((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f)))
% Found (and_rect00 (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found ((and_rect0 (P f)) (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found (((fun (P0:Type) (x0:((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->P0)))=> (((((and_rect (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))) P0) x0) x)) (P f)) (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found (((fun (P0:Type) (x0:((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->P0)))=> (((((and_rect (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))) P0) x0) x)) (P f)) (fun (x0:(cGVB_FUNCTION Xf))=> ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eq_ref00 (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found ((eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found (fun (x0:(cGVB_FUNCTION Xf))=> (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType))) as proof of (((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f))
% Found (fun (x0:(cGVB_FUNCTION Xf))=> (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType))) as proof of ((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P f)))
% Found (and_rect00 (fun (x0:(cGVB_FUNCTION Xf))=> (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found ((and_rect0 (P f)) (fun (x0:(cGVB_FUNCTION Xf))=> (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found (((fun (P0:Type) (x0:((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->P0)))=> (((((and_rect (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))) P0) x0) x)) (P f)) (fun (x0:(cGVB_FUNCTION Xf))=> (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found (((fun (P0:Type) (x0:((cGVB_FUNCTION Xf)->(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->P0)))=> (((((and_rect (cGVB_FUNCTION Xf)) ((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))) P0) x0) x)) (P f)) (fun (x0:(cGVB_FUNCTION Xf))=> (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)))) as proof of (P f)
% Found eq_ref00:=(eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))):(((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref000:=(eq_ref00 (ex fofType)):(((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eq_ref00 (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (ex fofType)) as proof of (P (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eq_ref00:=(eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))):(((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: b:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x4)):(((eq Prop) (f x4)) (f x4))
% Found (eq_ref0 (f x4)) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found ((eq_ref Prop) (f x4)) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (((eq Prop) (f x4)) ((and (cGVB_M x4)) (((eq fofType) ((cGVB_APPLY Xf) x4)) x4)))
% Found (fun (x4:fofType)=> ((eq_ref Prop) (f x4))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))->(P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))->(P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))->(P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))->(P0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) P0) as proof of (P1 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found (eq_ref0 ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) as proof of (((eq Prop) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found x5:((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Instantiate: b:=(fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))):(fofType->Prop)
% Found x5 as proof of (P b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eta_expansion_dep0 (fun (x7:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion_dep fofType) (fun (x7:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found x5:((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Instantiate: f:=(fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))):(fofType->Prop)
% Found x5 as proof of (P f)
% Found x5:((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Instantiate: f:=(fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))):(fofType->Prop)
% Found x5 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eq_ref00:=(eq_ref0 (f x6)):(((eq Prop) (f x6)) (f x6))
% Found (eq_ref0 (f x6)) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found ((eq_ref Prop) (f x6)) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (((eq Prop) (f x6)) ((and (cGVB_M x6)) (((eq fofType) ((cGVB_APPLY Xf) x6)) x6)))
% Found (fun (x6:fofType)=> ((eq_ref Prop) (f x6))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 (ex fofType)):(((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))->((ex fofType) (fun (x:fofType)=> ((and ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY x2) x)) x))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x)))))))
% Found (eta_expansion_dep000 (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (ex fofType)) as proof of (P (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (fun (x:fofType)=> ((and ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY x2) x)) x))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x))))))
% Found (eta_expansion_dep00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))):(((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) (fun (x:fofType)=> ((and ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY x2) x)) x))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x))))))
% Found (eta_expansion00 (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found ((eta_expansion0 Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) as proof of (((eq (fofType->Prop)) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx)))))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref00:=(eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))):(((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref00:=(eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))):(((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) as proof of (((eq (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P0 (fun (x:fofType)=> ((and ((and (cGVB_FUNCTION x)) ((cGVB_ITERATE Xf) x))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eta_expansion00 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eta_expansion0 Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P0 (fun (x:fofType)=> ((and ((and (cGVB_FUNCTION x)) ((cGVB_ITERATE Xf) x))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eta_expansion00 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eta_expansion0 Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((((eta_expansion fofType) Prop) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found eq_ref000:=(eq_ref00 P0):((P0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))->(P0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))))
% Found (eq_ref00 P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found ((eq_ref0 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found (((eq_ref (fofType->Prop)) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))) P0) as proof of (P1 (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: b:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))->(P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))))
% Found (eq_ref00 P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))->(P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))))
% Found (eq_ref00 P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))->(P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))))
% Found (eq_ref00 P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: b:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P b)
% Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))->(P0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))))
% Found (eq_ref00 P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found ((eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) P0) as proof of (P1 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found eq_ref00:=(eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))):(((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1)))
% Found (eq_ref0 ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found ((eq_ref Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) as proof of (((eq Prop) ((and (cGVB_M x1)) (((eq fofType) ((cGVB_APPLY Xf) x1)) x1))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and ((and (cGVB_FUNCTION x1)) ((cGVB_ITERATE Xf) x1))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x1) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x1) Xz)) Xz))->(((eq fofType) Xz) Xx))))))))
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found eq_ref00:=(eq_ref0 ((cGVB_APPLY Xf) x0)):(((eq fofType) ((cGVB_APPLY Xf) x0)) ((cGVB_APPLY Xf) x0))
% Found (eq_ref0 ((cGVB_APPLY Xf) x0)) as proof of (((eq fofType) ((cGVB_APPLY Xf) x0)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xf) x0)) as proof of (((eq fofType) ((cGVB_APPLY Xf) x0)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xf) x0)) as proof of (((eq fofType) ((cGVB_APPLY Xf) x0)) b)
% Found ((eq_ref fofType) ((cGVB_APPLY Xf) x0)) as proof of (((eq fofType) ((cGVB_APPLY Xf) x0)) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x0)
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found x1:((ex fofType) (fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))))
% Instantiate: f:=(fun (Xg:fofType)=> ((and ((and (cGVB_FUNCTION Xg)) ((cGVB_ITERATE Xf) Xg))) ((ex fofType) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY Xg) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY Xg) Xz)) Xz))->(((eq fofType) Xz) Xx)))))))):(fofType->Prop)
% Found x1 as proof of (P f)
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eq_ref00:=(eq_ref0 (f x8)):(((eq Prop) (f x8)) (f x8))
% Found (eq_ref0 (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found ((eq_ref Prop) (f x8)) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (((eq Prop) (f x8)) ((and (cGVB_M x8)) (((eq fofType) ((cGVB_APPLY Xf) x8)) x8)))
% Found (fun (x8:fofType)=> ((eq_ref Prop) (f x8))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion_dep00 b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found ((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found (((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xx:fofType)=> ((and ((and (cGVB_M Xx)) (((eq fofType) ((cGVB_APPLY x2) Xx)) Xx))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) Xx))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) b)
% Found x10:(cGVB_M x6)
% Instantiate: x12:=x6:fofType
% Found x10 as proof of (cGVB_M x12)
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found x11:(cGVB_M x7)
% Instantiate: x0:=x7:fofType
% Found x11 as proof of (cGVB_M x0)
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eta_expansion_dep0000:=(eta_expansion_dep000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion_dep000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion_dep00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion_dep0 (fun (x6:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion_dep fofType) (fun (x6:fofType)=> Prop)) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found eta_expansion0000:=(eta_expansion000 P0):((P0 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))->(P0 (fun (x:fofType)=> ((and (cGVB_M x)) (((eq fofType) ((cGVB_APPLY Xf) x)) x)))))
% Found (eta_expansion000 P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((eta_expansion00 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found (((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found ((((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy)))) P0) as proof of (P1 (fun (Xy:fofType)=> ((and (cGVB_M Xy)) (((eq fofType) ((cGVB_APPLY Xf) Xy)) Xy))))
% Found x11:(cGVB_M x7)
% Instantiate: x2:=x7:fofType
% Found x11 as proof of (cGVB_M x2)
% Found x11:(cGVB_M x7)
% Instantiate: x4:=x7:fofType
% Found x11 as proof of (cGVB_M x4)
% Found x11:(cGVB_M x7)
% Instantiate: x6:=x7:fofType
% Found x11 as proof of (cGVB_M x6)
% Found x11:(cGVB_M x6)
% Instantiate: x8:=x6:fofType
% Found x11 as proof of (cGVB_M x8)
% Found x11:(cGVB_M x6)
% Instantiate: x10:=x6:fofType
% Found x11 as proof of (cGVB_M x10)
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))):(((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))):(((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))):(((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found eq_ref00:=(eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))):(((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found ((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) as proof of (((eq Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY Xf) x5)) x5)))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))->(P0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found ((eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))->(P0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found ((eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found (((eq_ref Prop) ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))) P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found eq_ref000:=(eq_ref00 P0):((P0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))->(P0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5))))))
% Found (eq_ref00 P0) as proof of (P1 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x5)) x5))) (forall (Xz:fofType), (((and (cGVB_M Xz)) (((eq fofType) ((cGVB_APPLY x2) Xz)) Xz))->(((eq fofType) Xz) x5)))))
% Found ((eq_ref0 ((and ((and (cGVB_M x5)) (((eq fofType) ((cGVB_APPLY x2) x
% EOF
%------------------------------------------------------------------------------