%------------------------------------------------------------------------------
% File     : cocATP---0.2.0
% Problem  : SEV357^5 : TPTP v6.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p

% Computer : n097.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 13:34:05 EDT 2014

% Result   : Timeout 300.09s
% Output   : None 
% Verified : 
% SZS Type : None (Parsing solution fails)
% Syntax   : Number of formulae    : 0

% Comments : 
%------------------------------------------------------------------------------
%----NO SOLUTION OUTPUT BY SYSTEM
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% % Problem  : SEV357^5 : TPTP v6.1.0. Released v4.0.0.
% % Command  : python CASC.py /export/starexec/sandbox/benchmark/theBenchmark.p
% % Computer : n097.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 08:55:56 CDT 2014
% % CPUTime  : 300.09 
% 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 0x1edd830>, <kernel.DependentProduct object at 0x1eddf38>) of role type named cGVB_OP
% Using role type
% Declaring cGVB_OP:(fofType->(fofType->fofType))
% FOF formula (<kernel.Constant object at 0x20b1200>, <kernel.DependentProduct object at 0x1eddf38>) of role type named cGVB_IN
% Using role type
% Declaring cGVB_IN:(fofType->(fofType->Prop))
% FOF formula (<kernel.Constant object at 0x1edddd0>, <kernel.DependentProduct object at 0x1eddef0>) of role type named cGVB_M
% Using role type
% Declaring cGVB_M:(fofType->Prop)
% FOF formula (<kernel.Constant object at 0x1eddd40>, <kernel.Single object at 0x1eddf38>) of role type named cGVB_ZERO
% Using role type
% Declaring cGVB_ZERO:fofType
% FOF formula (<kernel.Constant object at 0x1edd908>, <kernel.DependentProduct object at 0x1edd5f0>) of role type named cGVB_FUNCTION
% Using role type
% Declaring cGVB_FUNCTION:(fofType->Prop)
% FOF formula ((ex fofType) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) of role conjecture named cGVB_E
% Conjecture to prove = ((ex fofType) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))):Prop
% We need to prove ['((ex fofType) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))']
% Parameter fofType:Type.
% Parameter cGVB_OP:(fofType->(fofType->fofType)).
% Parameter cGVB_IN:(fofType->(fofType->Prop)).
% Parameter cGVB_M:(fofType->Prop).
% Parameter cGVB_ZERO:fofType.
% Parameter cGVB_FUNCTION:(fofType->Prop).
% Trying to prove ((ex fofType) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))
% Found eta_expansion000:=(eta_expansion00 (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) (fun (x:fofType)=> ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))))
% Found (eta_expansion00 (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b)
% Found ((eta_expansion0 Prop) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b)
% Found (((eta_expansion fofType) Prop) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) ((and (cGVB_FUNCTION x)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))))
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) 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 (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))
% Found eq_ref00:=(eq_ref0 (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))):(((eq Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))
% Found (eq_ref0 (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) as proof of (((eq Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) as proof of (((eq Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) as proof of (((eq Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) b)
% Found ((eq_ref Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) as proof of (((eq Prop) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))))) b)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found eq_ref00:=(eq_ref0 (f x00)):(((eq Prop) (f x00)) (f x00))
% Found (eq_ref0 (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found ((eq_ref Prop) (f x00)) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (((eq Prop) (f x00)) ((and ((and (cGVB_M x00)) ((cGVB_IN x00) Xx))) ((cGVB_IN ((cGVB_OP Xx) x00)) x)))
% Found (fun (x00:fofType)=> ((eq_ref Prop) (f x00))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found (eq_ref0 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found ((eq_ref (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b)
% Found eq_ref00:=(eq_ref0 (f x02)):(((eq Prop) (f x02)) (f x02))
% Found (eq_ref0 (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found eq_ref00:=(eq_ref0 (f x02)):(((eq Prop) (f x02)) (f x02))
% Found (eq_ref0 (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found iff_refl:=(fun (A:Prop)=> ((((conj (A->A)) (A->A)) (fun (H:A)=> H)) (fun (H:A)=> H))):(forall (P:Prop), ((iff P) P))
% Instantiate: b:=(forall (P:Prop), ((iff P) P)):Prop
% Found iff_refl as proof of b
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))))))
% 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) b0)
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% 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 ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 a):(((eq (fofType->Prop)) a) (fun (x:fofType)=> (a x)))
% Found (eta_expansion_dep00 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN ((cGVB_OP Xx) x00)) x)):(((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found (eq_ref0 ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) b)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found eq_ref00:=(eq_ref0 a):(((eq (fofType->Prop)) a) a)
% Found (eq_ref0 a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) b)
% Found ((eq_ref (fofType->Prop)) a) as proof of (((eq (fofType->Prop)) a) 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 ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x))))
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found eq_ref00:=(eq_ref0 ((cGVB_IN ((cGVB_OP Xx) x02)) x)):(((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) ((cGVB_IN ((cGVB_OP Xx) x02)) x))
% Found (eq_ref0 ((cGVB_IN ((cGVB_OP Xx) x02)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x02)) x)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN ((cGVB_OP Xx) x00)) x)):(((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found (eq_ref0 ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) b)
% Found ((eq_ref Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) as proof of (((eq Prop) ((cGVB_IN ((cGVB_OP Xx) x00)) x)) 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) b0)
% Found ((eta_expansion_dep0 (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion_dep fofType) (fun (x1:fofType)=> Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: x00:=Xx:fofType;b:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop
% Found x0 as proof of (P b)
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x)):(((eq Prop) (f0 x)) (f0 x))
% Found (eq_ref0 (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found ((eq_ref Prop) (f0 x)) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (((eq Prop) (f0 x)) (f x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f0 x))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 ((cGVB_IN x00) Xx)):(((eq Prop) ((cGVB_IN x00) Xx)) ((cGVB_IN x00) Xx))
% Found (eq_ref0 ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) x)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: x02:=Xx:fofType;b:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop
% Found x0 as proof of (P b)
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: x00:=Xx:fofType;b:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop
% Found x0 as proof of (P b)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN x02) Xx)):(((eq Prop) ((cGVB_IN x02) Xx)) ((cGVB_IN x02) Xx))
% Found (eq_ref0 ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN x00) Xx)):(((eq Prop) ((cGVB_IN x00) Xx)) ((cGVB_IN x00) Xx))
% Found (eq_ref0 ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: x00:=Xx:fofType;b:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop
% Found x0 as proof of (P b)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN x00) Xx)):(((eq Prop) ((cGVB_IN x00) Xx)) ((cGVB_IN x00) Xx))
% Found (eq_ref0 ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 x):(((eq fofType) x) x)
% Found (eq_ref0 x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found ((eq_ref fofType) x) as proof of (((eq fofType) x) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_substitution:=(fun (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq U) (f a)) (f x)))) ((eq_ref U) (f a)))):(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b))))
% Instantiate: b:=(forall (T:Type) (U:Type) (a:T) (b:T) (f:(T->U)), ((((eq T) a) b)->(((eq U) (f a)) (f b)))):Prop
% Found eq_substitution as proof of b
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: b:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of b
% Found eq_sym as proof of a
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) Xx)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% Found choice_operator:=(fun (A:Type) (a:A)=> ((((classical_choice (A->Prop)) A) (fun (x3:(A->Prop))=> x3)) a)):(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P))))))))
% Instantiate: b:=(forall (A:Type), (A->((ex ((A->Prop)->A)) (fun (co:((A->Prop)->A))=> (forall (P:(A->Prop)), (((ex A) (fun (x:A)=> (P x)))->(P (co P)))))))):Prop
% Found choice_operator as proof of b
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found eq_ref00:=(eq_ref0 Xx):(((eq fofType) Xx) Xx)
% Found (eq_ref0 Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found ((eq_ref fofType) Xx) as proof of (((eq fofType) Xx) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x0:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x0 as proof of (cGVB_M x02)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found eq_ref00:=(eq_ref0 (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))):(((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu)))))))))
% Found (eq_ref0 (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b0)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b0)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b0)
% Found ((eq_ref (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) as proof of (((eq (fofType->Prop)) (fun (Xu:fofType)=> ((and (cGVB_FUNCTION Xu)) (forall (Xx:fofType), (((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))->((ex fofType) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) Xu))))))))) b0)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x0:=Xx:fofType
% Found x1 as proof of (cGVB_M x0)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: a:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of a
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found x0:(P2 (f x))
% Instantiate: f0:=f:(fofType->Prop)
% Found (fun (x0:(P2 (f x)))=> x0) as proof of (P2 (f0 x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of ((P2 (f x))->(P2 (f0 x)))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found x0:(P2 (f x))
% Instantiate: f0:=f:(fofType->Prop)
% Found (fun (x0:(P2 (f x)))=> x0) as proof of (P2 (f0 x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of ((P2 (f x))->(P2 (f0 x)))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x0:=Xx:fofType
% Found x1 as proof of (cGVB_M x0)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% 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) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x02)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x02)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x02)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x02)) x))
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN ((cGVB_OP Xx) x00)) x))
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x0:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x0)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x0))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x0)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found ((and_rect0 (cGVB_M x0)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x00)) (cGVB_M x0)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x00)) (cGVB_M x0)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: a:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop;x00:=Xx:fofType
% Found x0 as proof of (P a)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x01:(not (((eq fofType) Xx) cGVB_ZERO))
% Instantiate: b:=((((eq fofType) Xx) cGVB_ZERO)->False):Prop
% Found x01 as proof of a
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found x02:(not (((eq fofType) Xx) cGVB_ZERO))
% Instantiate: b:=((((eq fofType) Xx) cGVB_ZERO)->False):Prop
% Found x02 as proof of a
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) (fun (x0:fofType)=> ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found x2:(not (((eq fofType) Xx) cGVB_ZERO))
% Instantiate: b:=((((eq fofType) Xx) cGVB_ZERO)->False):Prop
% Found x2 as proof of a
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) (fun (x0:fofType)=> ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found conj20:=(conj2 (not (((eq fofType) Xx) cGVB_ZERO))):((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))))
% Found (conj2 (not (((eq fofType) Xx) cGVB_ZERO))) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->a))
% Found ((conj (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->a))
% Found ((conj (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->a))
% Found ((conj (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->a))
% Found (and_rect00 ((conj (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))) as proof of a
% Found ((and_rect0 a) ((conj (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))) as proof of a
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) a) ((conj (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))) as proof of a
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) a) ((conj (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))) as proof of a
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: a:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop;x02:=Xx:fofType
% Found x0 as proof of (P a)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: a:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop;x00:=Xx:fofType
% Found x0 as proof of (P a)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cGVB_IN x02) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x02) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x02) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x02) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x00 as proof of (cGVB_M x02)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x01:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x01 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x0:((and (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO)))
% Instantiate: a:=(not (((eq fofType) Xx) cGVB_ZERO)):Prop;x00:=Xx:fofType
% Found x0 as proof of (P a)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found eq_ref00:=(eq_ref0 (f x)):(((eq Prop) (f x)) (f x))
% Found (eq_ref0 (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found ((eq_ref Prop) (f x)) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType)=> ((eq_ref Prop) (f x))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_IN x00) Xx))->(P0 ((cGVB_IN x00) Xx)))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found ((eq_ref0 ((cGVB_IN x00) Xx)) P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found (((eq_ref Prop) ((cGVB_IN x00) Xx)) P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found (((eq_ref Prop) ((cGVB_IN x00) Xx)) P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found x0:(cGVB_M Xx)
% Instantiate: x02:=Xx:fofType
% Found x0 as proof of (cGVB_M x02)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN x00) Xx)):(((eq Prop) ((cGVB_IN x00) Xx)) ((cGVB_IN x00) Xx))
% Found (eq_ref0 ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x0:=Xx:fofType
% Found x1 as proof of (cGVB_M x0)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x0:(P2 (f x))
% Instantiate: f0:=f:(fofType->Prop)
% Found (fun (x0:(P2 (f x)))=> x0) as proof of (P2 (f0 x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of ((P2 (f x))->(P2 (f0 x)))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found x0:(P2 (f x))
% Instantiate: f0:=f:(fofType->Prop)
% Found (fun (x0:(P2 (f x)))=> x0) as proof of (P2 (f0 x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of ((P2 (f x))->(P2 (f0 x)))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found x0:(P2 (f x))
% Instantiate: f0:=f:(fofType->Prop)
% Found (fun (x0:(P2 (f x)))=> x0) as proof of (P2 (f0 x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of ((P2 (f x))->(P2 (f0 x)))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found x0:(P2 (f x))
% Instantiate: f0:=f:(fofType->Prop)
% Found (fun (x0:(P2 (f x)))=> x0) as proof of (P2 (f0 x))
% Found (fun (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of ((P2 (f x))->(P2 (f0 x)))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (((eq Prop) (f x)) (f0 x))
% Found (fun (x:fofType) (P2:(Prop->Prop)) (x0:(P2 (f x)))=> x0) as proof of (forall (x:fofType), (((eq Prop) (f x)) (f0 x)))
% Found or_comm_i:=(fun (A:Prop) (B:Prop) (H:((or A) B))=> ((((((or_ind A) B) ((or B) A)) ((or_intror B) A)) ((or_introl B) A)) H)):(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A)))
% Instantiate: a:=(forall (A:Prop) (B:Prop), (((or A) B)->((or B) A))):Prop
% Found or_comm_i as proof of a
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) ((cGVB_IN x00) Xx))
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 a):(((eq Prop) a) a)
% Found (eq_ref0 a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found ((eq_ref Prop) a) as proof of (((eq Prop) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) (fun (x0:fofType)=> ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found (eta_expansion_dep00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x1:(cGVB_M Xx)
% Instantiate: x3:=Xx:fofType
% Found x1 as proof of (cGVB_M x3)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found x1 as proof of (cGVB_M x00)
% Found x00:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x00 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x1)):(((eq Prop) (f0 x1)) (f0 x1))
% Found (eq_ref0 (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found ((eq_ref Prop) (f0 x1)) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (((eq Prop) (f0 x1)) (f x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f0 x1))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x1:(cGVB_M Xx)
% Instantiate: x0:=Xx:fofType
% Found x1 as proof of (cGVB_M x0)
% Found eq_ref00:=(eq_ref0 (f x02)):(((eq Prop) (f x02)) (f x02))
% Found (eq_ref0 (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found eq_ref00:=(eq_ref0 (f x02)):(((eq Prop) (f x02)) (f x02))
% Found (eq_ref0 (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found ((eq_ref Prop) (f x02)) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (((eq Prop) (f x02)) ((and ((and (cGVB_M x02)) ((cGVB_IN x02) Xx))) ((cGVB_IN ((cGVB_OP Xx) x02)) x)))
% Found (fun (x02:fofType)=> ((eq_ref Prop) (f x02))) as proof of (forall (x0:fofType), (((eq Prop) (f x0)) ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) x)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x2:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_IN x02) Xx))->(P0 ((cGVB_IN x02) Xx)))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_IN x02) Xx))
% Found ((eq_ref0 ((cGVB_IN x02) Xx)) P0) as proof of (P1 ((cGVB_IN x02) Xx))
% Found (((eq_ref Prop) ((cGVB_IN x02) Xx)) P0) as proof of (P1 ((cGVB_IN x02) Xx))
% Found (((eq_ref Prop) ((cGVB_IN x02) Xx)) P0) as proof of (P1 ((cGVB_IN x02) Xx))
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN x02) Xx)):(((eq Prop) ((cGVB_IN x02) Xx)) ((cGVB_IN x02) Xx))
% Found (eq_ref0 ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x02) Xx)) as proof of (((eq Prop) ((cGVB_IN x02) Xx)) b0)
% Found x1:(cGVB_M Xx)
% Instantiate: x00:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x00)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x00)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found ((and_rect0 (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x0)) (cGVB_M x00)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x00)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref000:=(eq_ref00 P0):((P0 ((cGVB_IN x00) Xx))->(P0 ((cGVB_IN x00) Xx)))
% Found (eq_ref00 P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found ((eq_ref0 ((cGVB_IN x00) Xx)) P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found (((eq_ref Prop) ((cGVB_IN x00) Xx)) P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found (((eq_ref Prop) ((cGVB_IN x00) Xx)) P0) as proof of (P1 ((cGVB_IN x00) Xx))
% Found x1:(cGVB_M Xx)
% Instantiate: x0:=Xx:fofType
% Found (fun (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of (cGVB_M x0)
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x0))
% Found (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x0)))
% Found (and_rect00 (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found ((and_rect0 (cGVB_M x0)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x00)) (cGVB_M x0)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found (((fun (P0:Type) (x1:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x1) x00)) (cGVB_M x0)) (fun (x1:(cGVB_M Xx)) (x2:(not (((eq fofType) Xx) cGVB_ZERO)))=> x1)) as proof of (cGVB_M x0)
% Found eq_ref00:=(eq_ref0 b):(((eq (fofType->Prop)) b) b)
% Found (eq_ref0 b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eq_ref (fofType->Prop)) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found x2 as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) b)
% Found eq_ref00:=(eq_ref0 ((cGVB_IN x00) Xx)):(((eq Prop) ((cGVB_IN x00) Xx)) ((cGVB_IN x00) Xx))
% Found (eq_ref0 ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found ((eq_ref Prop) ((cGVB_IN x00) Xx)) as proof of (((eq Prop) ((cGVB_IN x00) Xx)) b0)
% Found x01:(not (((eq fofType) Xx) cGVB_ZERO))
% Instantiate: b:=((((eq fofType) Xx) cGVB_ZERO)->False):Prop
% Found x01 as proof of a
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion000:=(eta_expansion00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion0 Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion fofType) Prop) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 b0):(((eq Prop) b0) b0)
% Found (eq_ref0 b0) as proof of (((eq Prop) b0) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cGVB_IN x00) Xx))
% Found ((eq_ref Prop) b0) as proof of (((eq Prop) b0) ((cGVB_IN x00) Xx))
% Found eq_ref00:=(eq_ref0 b):(((eq Prop) b) b)
% Found (eq_ref0 b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found ((eq_ref Prop) b) as proof of (((eq Prop) b) b0)
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 f):(((eq (fofType->Prop)) f) f)
% Found (eq_ref0 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eq_ref (fofType->Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eta_expansion_dep000:=(eta_expansion_dep00 f):(((eq (fofType->Prop)) f) (fun (x:fofType)=> (f x)))
% Found (eta_expansion_dep00 f) as proof of (((eq (fofType->Prop)) f) b)
% Found ((eta_expansion_dep0 (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found (((eta_expansion_dep fofType) (fun (x4:fofType)=> Prop)) f) as proof of (((eq (fofType->Prop)) f) b)
% Found eq_ref00:=(eq_ref0 (f x1)):(((eq Prop) (f x1)) (f x1))
% Found (eq_ref0 (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found ((eq_ref Prop) (f x1)) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (((eq Prop) (f x1)) (b x1))
% Found (fun (x1:fofType)=> ((eq_ref Prop) (f x1))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eta_expansion000:=(eta_expansion00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))):(((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) (fun (x0:fofType)=> ((and ((and (cGVB_M x0)) ((cGVB_IN x0) Xx))) ((cGVB_IN ((cGVB_OP Xx) x0)) x))))
% Found (eta_expansion00 (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found ((eta_expansion0 Prop) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found (((eta_expansion fofType) Prop) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) as proof of (((eq (fofType->Prop)) (fun (Xy:fofType)=> ((and ((and (cGVB_M Xy)) ((cGVB_IN Xy) Xx))) ((cGVB_IN ((cGVB_OP Xx) Xy)) x)))) b0)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found eq_ref00:=(eq_ref0 (f0 x3)):(((eq Prop) (f0 x3)) (f0 x3))
% Found (eq_ref0 (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found ((eq_ref Prop) (f0 x3)) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (((eq Prop) (f0 x3)) (f x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f0 x3))) as proof of (forall (x:fofType), (((eq Prop) (f0 x)) (f x)))
% Found x02:(not (((eq fofType) Xx) cGVB_ZERO))
% Instantiate: b:=((((eq fofType) Xx) cGVB_ZERO)->False):Prop
% Found x02 as proof of a
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eta_expansion000:=(eta_expansion00 b):(((eq (fofType->Prop)) b) (fun (x:fofType)=> (b x)))
% Found (eta_expansion00 b) as proof of (((eq (fofType->Prop)) b) b0)
% Found ((eta_expansion0 Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found (((eta_expansion fofType) Prop) b) as proof of (((eq (fofType->Prop)) b) b0)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_ref00:=(eq_ref0 (f x3)):(((eq Prop) (f x3)) (f x3))
% Found (eq_ref0 (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found ((eq_ref Prop) (f x3)) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (((eq Prop) (f x3)) (b x3))
% Found (fun (x3:fofType)=> ((eq_ref Prop) (f x3))) as proof of (forall (x:fofType), (((eq Prop) (f x)) (b x)))
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found x2:(cGVB_M Xx)
% Instantiate: x1:=Xx:fofType
% Found (fun (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of (cGVB_M x1)
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1))
% Found (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2) as proof of ((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->(cGVB_M x1)))
% Found (and_rect00 (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found ((and_rect0 (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found (((fun (P0:Type) (x2:((cGVB_M Xx)->((not (((eq fofType) Xx) cGVB_ZERO))->P0)))=> (((((and_rect (cGVB_M Xx)) (not (((eq fofType) Xx) cGVB_ZERO))) P0) x2) x0)) (cGVB_M x1)) (fun (x2:(cGVB_M Xx)) (x3:(not (((eq fofType) Xx) cGVB_ZERO)))=> x2)) as proof of (cGVB_M x1)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_ref00:=(eq_ref0 b):(((eq fofType) b) b)
% Found (eq_ref0 b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found ((eq_ref fofType) b) as proof of (((eq fofType) b) Xx)
% Found eq_ref00:=(eq_ref0 a):(((eq fofType) a) a)
% Found (eq_ref0 a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found ((eq_ref fofType) a) as proof of (((eq fofType) a) b)
% Found eq_sym:=(fun (T:Type) (a:T) (b:T) (H:(((eq T) a) b))=> ((H (fun (x:T)=> (((eq T) x) a))) ((eq_ref T) a))):(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a)))
% Instantiate: a:=(forall (T:Type) (a:T) (b:T), ((((eq T) a) b)->(((eq T) b) a))):Prop
% Found eq_sym as proof of a
% Found x2:(not (((eq fofType) Xx) cGVB_ZERO))
% Instantiate: b:=((((eq fofType) Xx) cGVB_ZERO)->False):Prop
% Found x2 as proof of a
% Found x2:(not (((eq fofType) Xx) cGVB_ZERO))
% Instantiate: b:=((((eq fofType) Xx) cGVB_ZERO)->Fals
% EOF
%------------------------------------------------------------------------------